On a \(p\)-Laplace Neumann problem with asymptotically asymmetric perturbations
The present paper deals with the elliptic problem of the form \[ \begin{gathered} -\Delta_p u= f(u)- h(x)\quad\text{in }\Omega,\\ {\partial \over\partial\nu}= 0\;\text{on}\;\partial\Omega,\end{gathered} \] where \(\Omega\subset\mathbb R^N\) is a bounded domain, \(\Delta_p\) is the \(p\)-Laplacian, \(p> 1\), \(h\in L^\infty(\Omega)\), \(f\in C(\mathbb R,\mathbb R)\). The goal of the authors is to improve and extend to the \(p\)-Laplacian well-known result for the Laplacian, in the case when \(f\) exhibits an asymmetric behaviour at infinity and may interact with the Dancer-Fučik spectrum.
scientific article; zbMATH DE number 1809997
scientific article