We consider a nonlinear Dirichlet equation driven by the sum of a p-Laplacian and of a Laplacian (a (p, 2)-equation). The hypotheses on the reaction f(z, x) are minimal and make the energy (Euler) functional of the problem coercive. We prove two multiplicity theorems producing three and four nontrivial smooth solutions, respectively, all with sign information. We apply our multiplicity results to the particular case of a class of parametric (p, 2)-equations.
Papageorgiou, N.S., Vetro, C., Vetro, F. (2020). Multiple Solutions with Sign Information for a Class of Coercive (p, 2)-Equations. BULLETIN OF THE MALAYSIAN MATHEMATICAL SOCIETY, 43(3), 2343-2371 [10.1007/s40840-019-00808-7].
Multiple Solutions with Sign Information for a Class of Coercive (p, 2)-Equations
Vetro, Calogero;
2020-01-01
Abstract
We consider a nonlinear Dirichlet equation driven by the sum of a p-Laplacian and of a Laplacian (a (p, 2)-equation). The hypotheses on the reaction f(z, x) are minimal and make the energy (Euler) functional of the problem coercive. We prove two multiplicity theorems producing three and four nontrivial smooth solutions, respectively, all with sign information. We apply our multiplicity results to the particular case of a class of parametric (p, 2)-equations.File | Dimensione | Formato | |
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