an:01837410
Zbl 1091.35025
Anello, Giovanni; Cordaro, Giuseppe
Existence of solutions of the Neumann problem for a class of equations involving the \(p\)-Laplacian via a variational principle of Ricceri
EN
Arch. Math. 79, No. 4, 274-287 (2002).
00088772
2002
j
35J60 35D05 35J20 35J25
Summary: In this paper we deal with the existence of weak solutions for the following Neumann problem
\[
\begin{cases} -\text{div}(| \nabla u| ^{p-2}\nabla u) + \lambda(x)| u| ^{p-2}u = \alpha(x)f(u) + \beta(x)g(u) \quad &\text{in }\Omega\\ \frac{\partial u}{\partial \nu} = 0 &\text{on }\partial \Omega \end{cases}
\]
where \(\nu \) is the outward unit normal to the boundary \(\partial\Omega \) of the bounded open set \(\Omega \subset \mathbb R^N\). The existence of solutions, for the above problem, is proved by applying a critical point theorem recently obtained by B. Ricceri as a consequence of a more general variational principle.