Eigenvalue problems for p(x)-Kirchhoff type equations
In this article, we study the nonlocal $p(x)$-Laplacian problem $$\displaylines{ -M\Big(\int_{\Omega}\frac{1}{p(x)}|\nabla u|^{p(x)}dx\Big) \hbox{div}(|\nabla u|^{p(x)-2}\nabla u)= \lambda|u|^{q(x)-2}u \quad \text{ in } \Omega,\cr u=0 \quad \text{on } \partial\Omega, }$$ By means of variation...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Texas State University
2013-11-01
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| Series: | Electronic Journal of Differential Equations |
| Subjects: | |
| Online Access: | http://ejde.math.txstate.edu/Volumes/2013/253/abstr.html |
| Summary: | In this article, we study the nonlocal $p(x)$-Laplacian problem
$$\displaylines{
-M\Big(\int_{\Omega}\frac{1}{p(x)}|\nabla u|^{p(x)}dx\Big)
\hbox{div}(|\nabla u|^{p(x)-2}\nabla u)= \lambda|u|^{q(x)-2}u \quad
\text{ in } \Omega,\cr
u=0 \quad \text{on } \partial\Omega,
}$$
By means of variational methods and the theory of the variable
exponent Sobolev spaces, we establish conditions for the
existence of weak solutions. |
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| ISSN: | 1072-6691 |