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EnglishWe consider a parametric nonlinear Dirichlet problem driven by the sum of a p-Laplacian and of a Laplacian (a (p,2)-equation) and with a reaction which has the competing effects of two distinct nonlinearities. A parametric term which is (p−1)-superlinear (convex term) and a perturbation which is (p−1)-sublinear (concave term). First we show that for all small values of the parameter the problem has at least five nontrivial smooth solutions, all with sign information. Then by strengthening the regularity of the two nonlinearities we produce two more nodal solutions, for a total of seven nontrivial smooth solutions all with sign informations. Our proofs use critical point theory, critical groups and flow invariance arguments.
Papageorgiou N.S., Vetro C., & Vetro F. (2020). Multiple solutions with sign information for a (p,2)-equation with combined nonlinearities. NONLINEAR ANALYSIS, 192, 1-25.
| Data di pubblicazione: | 2020 |
| Titolo: | Multiple solutions with sign information for a (p,2)-equation with combined nonlinearities |
| Autori: | |
| Citazione: | Papageorgiou N.S., Vetro C., & Vetro F. (2020). Multiple solutions with sign information for a (p,2)-equation with combined nonlinearities. NONLINEAR ANALYSIS, 192, 1-25. |
| Rivista: | |
| Digital Object Identifier (DOI): | http://dx.doi.org/10.1016/j.na.2019.111716 |
| Abstract: | We consider a parametric nonlinear Dirichlet problem driven by the sum of a p-Laplacian and of a Laplacian (a (p,2)-equation) and with a reaction which has the competing effects of two distinct nonlinearities. A parametric term which is (p−1)-superlinear (convex term) and a perturbation which is (p−1)-sublinear (concave term). First we show that for all small values of the parameter the problem has at least five nontrivial smooth solutions, all with sign information. Then by strengthening the regularity of the two nonlinearities we produce two more nodal solutions, for a total of seven nontrivial smooth solutions all with sign informations. Our proofs use critical point theory, critical groups and flow invariance arguments. |
| URL: | https://doi.org/10.1016/j.na.2019.111716 |
| Settore Scientifico Disciplinare: | Settore MAT/05 - Analisi Matematica |
| Appare nelle tipologie: | 1.01 Articolo in rivista |
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