Special Session 21: Variational, topological, and set-valued methods for differential problems
Contents
We present a collection of results on the existence and multiplicity of weak solutions for some elliptic problems involving the $p(\cdot)$-Laplace operator where $p \in C(\bar{\Omega})$ and $\Omega\subset {{\rm l}\kern-.17em{\rm R}} ^{N}$ is an open bounded domain with smooth boundary. In particular, under an appropriate oscillating behaviour of the nonlinearity $f$, the Neumann and Dirichlet problems will be studied in the case $1 < p^{-}\le p(x)\le p^{+}< +\infty$. The results are based on variational methods.