Noncoercive resonant (p,2)-equations with concave terms
| Autor: | Chao Zhang, Nikolaos S. Papageorgiou |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2018 |
| Předmět: |
nonlinear maximum principle
strong comparison principle QA299.6-433 truncation 010102 general mathematics Mathematical analysis Mathematics::Spectral Theory 35j20 01 natural sciences 58e05 35j60 010101 applied mathematics resonance nonlinear regularity theory 0101 mathematics constant sign and nodal solutions critical groups Geometry and topology concave term Analysis Mathematics |
| Zdroj: | Advances in Nonlinear Analysis, Vol 9, Iss 1, Pp 228-249 (2018) |
| Popis: | We consider a nonlinear Dirichlet problem driven by the sum of ap-Laplace and a Laplacian (a(p,2){(p,2)}-equation). The reaction exhibits the competing effects of a parametric concave term plus a Caratheodory perturbation which is resonant with respect to the principle eigenvalue of the Dirichletp-Laplacian. Using variational methods together with truncation and comparison techniques and Morse theory (critical groups), we show that for all small values of the parameter, the problem has as least six nontrivial smooth solutions all with sign information (two positive, two negative and two nodal (sign changing)). |
| Databáze: | OpenAIRE |
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