Nonlinear fourth order problems with asymptotically linear nonlinearities
| Autor: | Abir Amor Ben Ali, Makkia Dammak |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2024 |
| Předmět: | |
| Zdroj: | Mathematica Bohemica, Vol 149, Iss 2, Pp 209-223 (2024) |
| Druh dokumentu: | article |
| ISSN: | 0862-7959 2464-7136 |
| DOI: | 10.21136/MB.2023.0008-22 |
| Popis: | We investigate some nonlinear elliptic problems of the form \Delta^2v + \sigma(x) v= h(x,v)\quadin \Omega,\quad v=\Delta v=0 \quadon \partial\Omega, \eqno({\rm P}) where $\Omega$ is a regular bounded domain in $\mathbb{R}^N$, $N\geq2$, $\sigma(x)$ a positive function in $L^{\infty}(\Omega)$, and the nonlinearity $h(x,t)$ is indefinite. We prove the existence of solutions to the problem (P) when the function $h(x,t)$ is asymptotically linear at infinity by using variational method but without the Ambrosetti-Rabinowitz condition. Also, we consider the case when the nonlinearities are superlinear and subcritical. |
| Databáze: | Directory of Open Access Journals |
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