Opuscula Math. 35, no. 6 (2015), 889-905
http://dx.doi.org/10.7494/OpMath.2015.35.6.889

Opuscula Mathematica

# Existence and multiplicity of solutions for a nonhomogeneous Neumann boundary problem

Liliana Klimczak

Abstract. We consider a nonlinear Neumann elliptic equation driven by a $$p$$-Laplacian-type operator which is not homogeneous in general. For such an equation the energy functional does not need to be coercive, and we use suitable variational methods to show that the problem has at least two distinct, nontrivial smooth solutions. Our formulation incorporates strongly resonant equations.

Keywords: Palais-Smale condition, noncoercive functional, second deformation theorem.

Mathematics Subject Classification: 35J20, 35J60.

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• Liliana Klimczak
• Jagiellonian University, Faculty of Mathematics and Computer Science, ul. Łojasiewicza 6, 30-348 Krakow, Poland
• Communicated by Marek Galewski.
• Revised: 2015-02-02.
• Accepted: 2015-02-17.
• Published online: 2015-06-06.