Existence of a positive infimum eigenvalue for the $p(x)$-Laplacian Neumann problems with weighted functions
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Abstract
\begin{equation*}
-\text{div}(w(x)|\nabla u|^{p(x)-2}\nabla u)+|u|^{p(x)-2}u=\lambda f(x,u) \quad \text{in } \Omega
\end{equation*}
which is subject to Neumann boundary condition. Under suitable conditions on $w$ and $f$, we give the existence of a positive infimum eigenvalue for the $p(x)$-Laplacian Neumann problem.
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