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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
##### Keywords:
Neumann problem; $$p$$-Laplacian; Multiple solutions
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##### References:
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