HAL (Le Centre pour la Communication Scientifique Directe), 2007
We consider the problem: -div(p∇u) = u q-1 + λu, u > 0 in Ω, u = 0 on ∂Ω. Where Ω is a bounded do... more We consider the problem: -div(p∇u) = u q-1 + λu, u > 0 in Ω, u = 0 on ∂Ω. Where Ω is a bounded domain in IR n , n ≥ 3, p : Ω -→ IR is a given positive weight such that p ∈ H 1 (Ω) ∩ C( Ω), λ is a real constant and q = 2n n-2 . We study the effect of the behavior of p near its minima and the impact of the geometry of domain on the existence of solutions for the above problem.
The Journal of Nonlinear Sciences and Applications, Aug 10, 2013
In this paper, we establish a new fixed point theorem for a Meir-Keeler type contraction through ... more In this paper, we establish a new fixed point theorem for a Meir-Keeler type contraction through rational expression. The presented theorem is an extension of the result of . Some applications to contractions of integral type are given.
The journal of mathematics and computer science, Sep 15, 2010
In this paper, we introduce the notion of partially ordered ε-chainable metric spaces and we deri... more In this paper, we introduce the notion of partially ordered ε-chainable metric spaces and we derive new coupled fixed point theorems for uniformly locally contractive mappings on such spaces.
In this work, we study the two following minimization problems for r ∈ N * , S0,r(ϕ) = inf u∈H r ... more In this work, we study the two following minimization problems for r ∈ N * , S0,r(ϕ) = inf u∈H r 0 (Ω), u+ϕ L 2 * r =1 u 2 r and S θ,r (ϕ) = inf u∈H r θ (Ω), u+ϕ L 2 * r =1 u 2 r , where Ω ⊂ R N , N > 2r, is a smooth bounded domain, 2 * r = 2N N−2r , ϕ ∈ L 2 * r (Ω) ∩ C(Ω) and the norm. r = Ω |(−∆) α .| 2 dx where α = r 2 if r is even and. r = Ω |∇(−∆) α .| 2 dx where α = r−1 2 if r is odd. Firstly, we prove that, when ϕ ≡ 0, the infimum in S0,r(ϕ) and S θ,r (ϕ) are achieved. Secondly, we show that S θ,r (ϕ) < S0,r(ϕ) for a large class of ϕ.
In this work, we study the two following minimization problems for r ∈ N∗, S0,r(φ) = inf u∈H 0 (Ω... more In this work, we study the two following minimization problems for r ∈ N∗, S0,r(φ) = inf u∈H 0 (Ω), ‖u+φ‖ L2 ∗r =1 ‖u‖r and Sθ,r(φ) = inf u∈H θ (Ω), ‖u+φ‖ L2 ∗r =1 ‖u‖r , where Ω ⊂ RN , N > 2r, is a smooth bounded domain, 2∗r = 2N N−2r , φ ∈ L2 ∗r (Ω)∩C(Ω) and the norm ‖.‖r = ∫ Ω |(−∆).|dx where α = r 2 if r is even and ‖.‖r = ∫ Ω |∇(−∆).|dx where α = r−1 2 if r is odd. Firstly, we prove that, when φ 6≡ 0, the infimum in S0,r(φ) and Sθ,r(φ) are attained. Secondly, we show that Sθ,r(φ) < S0,r(φ) for a large class of φ.
We discuss the existence of solutions of nonlinear problem involving,two critical Sobolev exponen... more We discuss the existence of solutions of nonlinear problem involving,two critical Sobolev exponents. we will ll out the su cient conditions to nd solutions for the problem in presence of a nonlinear Neumann boundary data with a critical nonlinearity. \
In this paper, we introduce the notion of partially ordered ϵ-chainable metric spaces and we deri... more In this paper, we introduce the notion of partially ordered ϵ-chainable metric spaces and we derive new coupled fixed point theorems for uniformly locally contractive mappings on such spaces.
We study existence results for a problem with criticical Sobolev exponent and with a positive wei... more We study existence results for a problem with criticical Sobolev exponent and with a positive weight.
In this paper, we prove the existence of a positive solution for elliptic nonlinear partial diffe... more In this paper, we prove the existence of a positive solution for elliptic nonlinear partial differential equation with weight involving a critical exponent of Sobolev imbedding on S3. Moreover, we ...
In this paper, we introduce the concept of mixed (G, S)-monotone mappings and prove coupled coinc... more In this paper, we introduce the concept of mixed (G, S)-monotone mappings and prove coupled coincidence and coupled common fixed point theorems for such mappings satisfying a nonlinear contraction involving altering distance functions. Presented theorems extend, improve and generalize the very recent results of Harjani, López and Sadarangani [J. Harjani, B. López and K. Sadarangani, Fixed point theorems for mixed monotone operators and applications to integral equations, Nonlinear Analysis (2010),
We study the non-linear minimization problem on H 1 0 (Ω) ⊂ Lq with q = 2n inf (1+|x| ‖u‖Lq=1 Ω β... more We study the non-linear minimization problem on H 1 0 (Ω) ⊂ Lq with q = 2n inf (1+|x| ‖u‖Lq=1 Ω β |u | k)|∇u | 2. n−2: We show that minimizers exist only in the range β < kn/q which corresponds to a dominant nonlinear term. On the contrary, the linear influence for β ≥ kn/q prevents their existence.
In this paper, we introduce the concept of mixed (G, S)-monotone mappings and prove coupled coinc... more In this paper, we introduce the concept of mixed (G, S)-monotone mappings and prove coupled coincidence and coupled common fixed point theorems for such mappings satisfying a nonlinear contraction involving altering distance functions. Presented theorems extend, improve and generalize the very recent results of Harjani, L\'opez and Sadarangani [J. Harjani, B. L\'opez and K. Sadarangani, Fixed point theorems for mixed monotone operators and applications to integral equations, Nonlinear Analysis (2010), doi:10.1016/j.na.2010.10.047] and other existing results in the literature. Some applications to periodic boundary value problems are also considered.
We establish coupled fixed point theorems for contraction involving rational expressions in parti... more We establish coupled fixed point theorems for contraction involving rational expressions in partially ordered metric spaces.
In this paper, we introduce the notion of partially ordered {\epsilon}-chainable metric spaces an... more In this paper, we introduce the notion of partially ordered {\epsilon}-chainable metric spaces and we derive new coupled fixed point theorems for uniformly locally contractive mappings on such spaces.
We study the minimizing problem where is a smooth bounded domain of , and p a positive discontinu... more We study the minimizing problem where is a smooth bounded domain of , and p a positive discontinuous function. We prove the existence of a minimizer under some assumptions.
In this article, we prove the existence of solutions for a nonvariational system of elliptic PDE’... more In this article, we prove the existence of solutions for a nonvariational system of elliptic PDE’s. Also we study a system of bi-Laplacian equations with two nonlinearities and without variational assumptions. First, we prove a priori solution estimates, and then we use fixed point theory, to deduce the existence of solutions. Finally, to complement of the existence theorem, we establish a non-existence result.
We study the quasi-linear minimization problem on $H^1_0(\Omega)\subset L^q$ with $q=\frac{2n}{n-... more We study the quasi-linear minimization problem on $H^1_0(\Omega)\subset L^q$ with $q=\frac{2n}{n-2}$~: $$\inf_{\|u\|_{L^q}=1}\int_\Omega (1+|x|^\beta |u|^k)|\nabla u|^2.$$ We show that minimizers exist only in the range $\beta<kn/q$ which corresponds to a dominant non-linear term. On the contrary, the linear influence for $\beta\geq kn/q$ prevents their existence.
We study a system of bi-laplacian equations with a non-variational structure using fixed point th... more We study a system of bi-laplacian equations with a non-variational structure using fixed point theory. We prove some existence and non-existence results and we obtain some a priori estimates of solution.
In this paper, following the idea of Samet et al. (J. Nonlinear. Sci. Appl. 6:162-169, 2013), we ... more In this paper, following the idea of Samet et al. (J. Nonlinear. Sci. Appl. 6:162-169, 2013), we establish a new fixed point theorem for a Meir-Keeler type contraction via Gupta-Saxena rational expression which enables us to extend and generalize their main result (Gupta and Saxena in Math. Stud. 52:156-158, 1984). As an application we derive some fixed points of mappings of integral type.
We consider the problem: where Ω is a bounded smooth domain in R N , N ≥ 3. Under some conditions... more We consider the problem: where Ω is a bounded smooth domain in R N , N ≥ 3. Under some conditions on ∂Ω , p, Q, f , λ and the mean curvature at some point x 0 , we prove the existence of solutions of the above problem. We use variational arguments, namely Ekeland's variational principle, the min-max principle and the mountain pass theorem.
HAL (Le Centre pour la Communication Scientifique Directe), 2007
We consider the problem: -div(p∇u) = u q-1 + λu, u > 0 in Ω, u = 0 on ∂Ω. Where Ω is a bounded do... more We consider the problem: -div(p∇u) = u q-1 + λu, u > 0 in Ω, u = 0 on ∂Ω. Where Ω is a bounded domain in IR n , n ≥ 3, p : Ω -→ IR is a given positive weight such that p ∈ H 1 (Ω) ∩ C( Ω), λ is a real constant and q = 2n n-2 . We study the effect of the behavior of p near its minima and the impact of the geometry of domain on the existence of solutions for the above problem.
The Journal of Nonlinear Sciences and Applications, Aug 10, 2013
In this paper, we establish a new fixed point theorem for a Meir-Keeler type contraction through ... more In this paper, we establish a new fixed point theorem for a Meir-Keeler type contraction through rational expression. The presented theorem is an extension of the result of . Some applications to contractions of integral type are given.
The journal of mathematics and computer science, Sep 15, 2010
In this paper, we introduce the notion of partially ordered ε-chainable metric spaces and we deri... more In this paper, we introduce the notion of partially ordered ε-chainable metric spaces and we derive new coupled fixed point theorems for uniformly locally contractive mappings on such spaces.
In this work, we study the two following minimization problems for r ∈ N * , S0,r(ϕ) = inf u∈H r ... more In this work, we study the two following minimization problems for r ∈ N * , S0,r(ϕ) = inf u∈H r 0 (Ω), u+ϕ L 2 * r =1 u 2 r and S θ,r (ϕ) = inf u∈H r θ (Ω), u+ϕ L 2 * r =1 u 2 r , where Ω ⊂ R N , N > 2r, is a smooth bounded domain, 2 * r = 2N N−2r , ϕ ∈ L 2 * r (Ω) ∩ C(Ω) and the norm. r = Ω |(−∆) α .| 2 dx where α = r 2 if r is even and. r = Ω |∇(−∆) α .| 2 dx where α = r−1 2 if r is odd. Firstly, we prove that, when ϕ ≡ 0, the infimum in S0,r(ϕ) and S θ,r (ϕ) are achieved. Secondly, we show that S θ,r (ϕ) < S0,r(ϕ) for a large class of ϕ.
In this work, we study the two following minimization problems for r ∈ N∗, S0,r(φ) = inf u∈H 0 (Ω... more In this work, we study the two following minimization problems for r ∈ N∗, S0,r(φ) = inf u∈H 0 (Ω), ‖u+φ‖ L2 ∗r =1 ‖u‖r and Sθ,r(φ) = inf u∈H θ (Ω), ‖u+φ‖ L2 ∗r =1 ‖u‖r , where Ω ⊂ RN , N > 2r, is a smooth bounded domain, 2∗r = 2N N−2r , φ ∈ L2 ∗r (Ω)∩C(Ω) and the norm ‖.‖r = ∫ Ω |(−∆).|dx where α = r 2 if r is even and ‖.‖r = ∫ Ω |∇(−∆).|dx where α = r−1 2 if r is odd. Firstly, we prove that, when φ 6≡ 0, the infimum in S0,r(φ) and Sθ,r(φ) are attained. Secondly, we show that Sθ,r(φ) < S0,r(φ) for a large class of φ.
We discuss the existence of solutions of nonlinear problem involving,two critical Sobolev exponen... more We discuss the existence of solutions of nonlinear problem involving,two critical Sobolev exponents. we will ll out the su cient conditions to nd solutions for the problem in presence of a nonlinear Neumann boundary data with a critical nonlinearity. \
In this paper, we introduce the notion of partially ordered ϵ-chainable metric spaces and we deri... more In this paper, we introduce the notion of partially ordered ϵ-chainable metric spaces and we derive new coupled fixed point theorems for uniformly locally contractive mappings on such spaces.
We study existence results for a problem with criticical Sobolev exponent and with a positive wei... more We study existence results for a problem with criticical Sobolev exponent and with a positive weight.
In this paper, we prove the existence of a positive solution for elliptic nonlinear partial diffe... more In this paper, we prove the existence of a positive solution for elliptic nonlinear partial differential equation with weight involving a critical exponent of Sobolev imbedding on S3. Moreover, we ...
In this paper, we introduce the concept of mixed (G, S)-monotone mappings and prove coupled coinc... more In this paper, we introduce the concept of mixed (G, S)-monotone mappings and prove coupled coincidence and coupled common fixed point theorems for such mappings satisfying a nonlinear contraction involving altering distance functions. Presented theorems extend, improve and generalize the very recent results of Harjani, López and Sadarangani [J. Harjani, B. López and K. Sadarangani, Fixed point theorems for mixed monotone operators and applications to integral equations, Nonlinear Analysis (2010),
We study the non-linear minimization problem on H 1 0 (Ω) ⊂ Lq with q = 2n inf (1+|x| ‖u‖Lq=1 Ω β... more We study the non-linear minimization problem on H 1 0 (Ω) ⊂ Lq with q = 2n inf (1+|x| ‖u‖Lq=1 Ω β |u | k)|∇u | 2. n−2: We show that minimizers exist only in the range β < kn/q which corresponds to a dominant nonlinear term. On the contrary, the linear influence for β ≥ kn/q prevents their existence.
In this paper, we introduce the concept of mixed (G, S)-monotone mappings and prove coupled coinc... more In this paper, we introduce the concept of mixed (G, S)-monotone mappings and prove coupled coincidence and coupled common fixed point theorems for such mappings satisfying a nonlinear contraction involving altering distance functions. Presented theorems extend, improve and generalize the very recent results of Harjani, L\'opez and Sadarangani [J. Harjani, B. L\'opez and K. Sadarangani, Fixed point theorems for mixed monotone operators and applications to integral equations, Nonlinear Analysis (2010), doi:10.1016/j.na.2010.10.047] and other existing results in the literature. Some applications to periodic boundary value problems are also considered.
We establish coupled fixed point theorems for contraction involving rational expressions in parti... more We establish coupled fixed point theorems for contraction involving rational expressions in partially ordered metric spaces.
In this paper, we introduce the notion of partially ordered {\epsilon}-chainable metric spaces an... more In this paper, we introduce the notion of partially ordered {\epsilon}-chainable metric spaces and we derive new coupled fixed point theorems for uniformly locally contractive mappings on such spaces.
We study the minimizing problem where is a smooth bounded domain of , and p a positive discontinu... more We study the minimizing problem where is a smooth bounded domain of , and p a positive discontinuous function. We prove the existence of a minimizer under some assumptions.
In this article, we prove the existence of solutions for a nonvariational system of elliptic PDE’... more In this article, we prove the existence of solutions for a nonvariational system of elliptic PDE’s. Also we study a system of bi-Laplacian equations with two nonlinearities and without variational assumptions. First, we prove a priori solution estimates, and then we use fixed point theory, to deduce the existence of solutions. Finally, to complement of the existence theorem, we establish a non-existence result.
We study the quasi-linear minimization problem on $H^1_0(\Omega)\subset L^q$ with $q=\frac{2n}{n-... more We study the quasi-linear minimization problem on $H^1_0(\Omega)\subset L^q$ with $q=\frac{2n}{n-2}$~: $$\inf_{\|u\|_{L^q}=1}\int_\Omega (1+|x|^\beta |u|^k)|\nabla u|^2.$$ We show that minimizers exist only in the range $\beta<kn/q$ which corresponds to a dominant non-linear term. On the contrary, the linear influence for $\beta\geq kn/q$ prevents their existence.
We study a system of bi-laplacian equations with a non-variational structure using fixed point th... more We study a system of bi-laplacian equations with a non-variational structure using fixed point theory. We prove some existence and non-existence results and we obtain some a priori estimates of solution.
In this paper, following the idea of Samet et al. (J. Nonlinear. Sci. Appl. 6:162-169, 2013), we ... more In this paper, following the idea of Samet et al. (J. Nonlinear. Sci. Appl. 6:162-169, 2013), we establish a new fixed point theorem for a Meir-Keeler type contraction via Gupta-Saxena rational expression which enables us to extend and generalize their main result (Gupta and Saxena in Math. Stud. 52:156-158, 1984). As an application we derive some fixed points of mappings of integral type.
We consider the problem: where Ω is a bounded smooth domain in R N , N ≥ 3. Under some conditions... more We consider the problem: where Ω is a bounded smooth domain in R N , N ≥ 3. Under some conditions on ∂Ω , p, Q, f , λ and the mean curvature at some point x 0 , we prove the existence of solutions of the above problem. We use variational arguments, namely Ekeland's variational principle, the min-max principle and the mountain pass theorem.
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