Eigenvalues of the $p(x)-$biharmonic operator with indefinite weight] {Eigenvalues of the $p(x)-$biharmonic operator with indefinite weight under Neumann boundary conditions
In this paper we will study the existence of solutions for the nonhomogeneous elliptic equation with variable exponent $\Delta^2_{p(x)} u=\lambda V(x) |u|^{q(x)-2} u$, in a smooth bounded domain,under Neumann boundary conditions, where $\lambda$ is a positive real number, $p,q: \overline{\Omega} \ri...
| Main Authors: | , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Sociedade Brasileira de Matemática
2018-01-01
|
| Series: | Boletim da Sociedade Paranaense de Matemática |
| Subjects: | |
| Online Access: | http://periodicos.uem.br/ojs/index.php/BSocParanMat/article/view/31363 |
| Summary: | In this paper we will study the existence of solutions for the nonhomogeneous elliptic equation with variable exponent $\Delta^2_{p(x)} u=\lambda V(x) |u|^{q(x)-2} u$, in a smooth bounded domain,under Neumann boundary conditions, where $\lambda$ is a positive real number, $p,q: \overline{\Omega} \rightarrow \mathbb{R}$, are continuous functions, and $V$ is an indefinite weight function. Considering different situations concerning the growth rates involved in the above quoted problem, we will prove the existence of a continuous family of eigenvalues. |
|---|---|
| ISSN: | 0037-8712 2175-1188 |