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Multiplicity results for a Neumann problem involving the \(p\)-Laplacian. (English) Zbl 1092.35033
Summary: In this paper we establish some multiplicity results for the following Neumann problem:
\[ -\text{div}(|\nabla u|^{p-2}\nabla u)+\lambda(x)|u|^{p-2}u=\alpha(x) f(u) \quad\text{in }\Omega, \]
\[ \partial u/\partial \nu=0 \quad\text{ on } \Omega. \]
The multiple solutions are obtained by combining an existence theorem recently proved by G. Anello and G. Cordaro [ J. Convex Anal. 10, No. 1, 185–198 (2003; Zbl 1091.35026)] with well-known critical point theorems.

MSC:
35J60 Nonlinear elliptic equations
35J25 Boundary value problems for second-order elliptic equations
35J50 Variational methods for elliptic systems
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