The work deals with Morse index estimates for a solution u ∈ H p 1 (M ) of the quasilinear ellipt... more The work deals with Morse index estimates for a solution u ∈ H p 1 (M ) of the quasilinear elliptic equation −div g (α + |∇u| g 2)
In this work we study a class of functionals, defined on Banach spaces, associated with quasiline... more In this work we study a class of functionals, defined on Banach spaces, associated with quasilinear elliptic systems. Firstly, we prove some regularity results about the critical points of such functionals and then we estimate the critical groups in each critical point via its Morse index.
We consider a class of quasilinear elliptic equations whose principal part includes the p-area (f... more We consider a class of quasilinear elliptic equations whose principal part includes the p-area (for 1 < p < ∞) and the p-Laplace (for 1 < p ≤ 2) operator. For the critical points of the associated functional, we provide estimates of the corresponding critical polynomial.
In this work we consider a class of Euler functionals defined in Banach spaces, associated to qua... more In this work we consider a class of Euler functionals defined in Banach spaces, associated to quasilinear elliptic problems involving the critical Sobolev exponent. We perform critical groups estimates via the Morse index.
In this work we study a class of functionals, defined on Banach spaces, associated with quasiline... more In this work we study a class of functionals, defined on Banach spaces, associated with quasilinear elliptic systems. Firstly, we prove some regularity results about the critical points of such functionals and then we estimate the critical groups in each critical point via its Morse index.
Rendiconti Lincei - Matematica e Applicazioni, 2015
We consider a class of quasilinear elliptic equations whose principal part includes the p-area (f... more We consider a class of quasilinear elliptic equations whose principal part includes the p-area (for 1 < p < ∞) and the p-Laplace (for 1 < p ≤ 2) operator. For the critical points of the associated functional, we provide estimates of the corresponding critical polynomial.
In this work we prove some multiplicity results for solutions of a system of elliptic quasilinear... more In this work we prove some multiplicity results for solutions of a system of elliptic quasilinear equations, involving the p-Laplace operator (p > 2). The proofs are based on variational and topological arguments and make use of new perturbation results in Morse theory for the Banach space W 1,p 0 . MSC 2000: 58E05, 35B20, 35J50
In this work we consider a class of Euler functionals defined in Banach spaces, associated to qua... more In this work we consider a class of Euler functionals defined in Banach spaces, associated to quasilinear elliptic problems involving the critical Sobolev exponent. We perform critical groups estimates via the Morse index.
In this work we study a class of Euler functionals defined in Banach spaces, associated with quas... more In this work we study a class of Euler functionals defined in Banach spaces, associated with quasilinear elliptic problems involving p-Laplace operator (p > 2). First we obtain perturbation results in the spirit of the remarkable paper by Marino and Prodi [26], using the new definition of nondegeneracy given in . We also extend Morse index estimates for minimax critical points, introduced by Lazer and Solimini in the Hilbert case, to our Banach setting.
Regularity results and critical group estimates are studied for critical (p, r)-systems. Multipli... more Regularity results and critical group estimates are studied for critical (p, r)-systems. Multiplicity results of solutions for a critical potential quasilinear system are also proved using Morse theory.
In this paper we study regularity and partial regularity for the weak solution of a class of gene... more In this paper we study regularity and partial regularity for the weak solution of a class of general quasi-linear elliptic equations and systems, which are of the quasi-linear main coefficients satisfying the VMO conditions in x uniformly with respect to u, and of the lower order items satisfying controllable growth.
Communications in Partial Differential Equations, 2013
Regularity results and critical group estimates are studied for critical (p, r)-systems. Multipli... more Regularity results and critical group estimates are studied for critical (p, r)-systems. Multiplicity results of solutions for a critical potential quasilinear system are also proved using Morse theory.
In this work we study a class of functionals, defined on Banach spaces, associated with quasiline... more In this work we study a class of functionals, defined on Banach spaces, associated with quasilinear elliptic systems. Firstly, we prove some regularity results about the critical points of such functionals and then we estimate the critical groups in each critical point via its Morse index.
The work deals with Morse index estimates for a solution u ∈ H p 1 (M ) of the quasilinear ellipt... more The work deals with Morse index estimates for a solution u ∈ H p 1 (M ) of the quasilinear elliptic equation −div g (α + |∇u| g 2)
The work deals with Morse index estimates for a solution u ∈ H p 1 (M ) of the quasilinear ellipt... more The work deals with Morse index estimates for a solution u ∈ H p 1 (M ) of the quasilinear elliptic equation −div g (α + |∇u| g 2)
In this work we study a class of functionals, defined on Banach spaces, associated with quasiline... more In this work we study a class of functionals, defined on Banach spaces, associated with quasilinear elliptic systems. Firstly, we prove some regularity results about the critical points of such functionals and then we estimate the critical groups in each critical point via its Morse index.
We consider a class of quasilinear elliptic equations whose principal part includes the p-area (f... more We consider a class of quasilinear elliptic equations whose principal part includes the p-area (for 1 < p < ∞) and the p-Laplace (for 1 < p ≤ 2) operator. For the critical points of the associated functional, we provide estimates of the corresponding critical polynomial.
In this work we consider a class of Euler functionals defined in Banach spaces, associated to qua... more In this work we consider a class of Euler functionals defined in Banach spaces, associated to quasilinear elliptic problems involving the critical Sobolev exponent. We perform critical groups estimates via the Morse index.
In this work we study a class of functionals, defined on Banach spaces, associated with quasiline... more In this work we study a class of functionals, defined on Banach spaces, associated with quasilinear elliptic systems. Firstly, we prove some regularity results about the critical points of such functionals and then we estimate the critical groups in each critical point via its Morse index.
Rendiconti Lincei - Matematica e Applicazioni, 2015
We consider a class of quasilinear elliptic equations whose principal part includes the p-area (f... more We consider a class of quasilinear elliptic equations whose principal part includes the p-area (for 1 < p < ∞) and the p-Laplace (for 1 < p ≤ 2) operator. For the critical points of the associated functional, we provide estimates of the corresponding critical polynomial.
In this work we prove some multiplicity results for solutions of a system of elliptic quasilinear... more In this work we prove some multiplicity results for solutions of a system of elliptic quasilinear equations, involving the p-Laplace operator (p > 2). The proofs are based on variational and topological arguments and make use of new perturbation results in Morse theory for the Banach space W 1,p 0 . MSC 2000: 58E05, 35B20, 35J50
In this work we consider a class of Euler functionals defined in Banach spaces, associated to qua... more In this work we consider a class of Euler functionals defined in Banach spaces, associated to quasilinear elliptic problems involving the critical Sobolev exponent. We perform critical groups estimates via the Morse index.
In this work we study a class of Euler functionals defined in Banach spaces, associated with quas... more In this work we study a class of Euler functionals defined in Banach spaces, associated with quasilinear elliptic problems involving p-Laplace operator (p > 2). First we obtain perturbation results in the spirit of the remarkable paper by Marino and Prodi [26], using the new definition of nondegeneracy given in . We also extend Morse index estimates for minimax critical points, introduced by Lazer and Solimini in the Hilbert case, to our Banach setting.
Regularity results and critical group estimates are studied for critical (p, r)-systems. Multipli... more Regularity results and critical group estimates are studied for critical (p, r)-systems. Multiplicity results of solutions for a critical potential quasilinear system are also proved using Morse theory.
In this paper we study regularity and partial regularity for the weak solution of a class of gene... more In this paper we study regularity and partial regularity for the weak solution of a class of general quasi-linear elliptic equations and systems, which are of the quasi-linear main coefficients satisfying the VMO conditions in x uniformly with respect to u, and of the lower order items satisfying controllable growth.
Communications in Partial Differential Equations, 2013
Regularity results and critical group estimates are studied for critical (p, r)-systems. Multipli... more Regularity results and critical group estimates are studied for critical (p, r)-systems. Multiplicity results of solutions for a critical potential quasilinear system are also proved using Morse theory.
In this work we study a class of functionals, defined on Banach spaces, associated with quasiline... more In this work we study a class of functionals, defined on Banach spaces, associated with quasilinear elliptic systems. Firstly, we prove some regularity results about the critical points of such functionals and then we estimate the critical groups in each critical point via its Morse index.
The work deals with Morse index estimates for a solution u ∈ H p 1 (M ) of the quasilinear ellipt... more The work deals with Morse index estimates for a solution u ∈ H p 1 (M ) of the quasilinear elliptic equation −div g (α + |∇u| g 2)
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