We study the existence and multiplicity of weak solutions for a parametric Neumann problem driven by the p(x)-Laplacian. Under a suitable condition on the behavior of the potential at 0^+, we obtain an interval such that when a parameter lambda is in this interval, our problem admits at least one nontrivial weak solution. We show the multiplicity of solutions for potentials satisfying also the Ambrosetti-Rabinowitz condition. Moreover, if the right-hand side f satisfies the Ambrosetti-Rabinowitz condition, then we obtain the existence of two nontrivial weak solutions.

Existence of solutions for a Neumann problem involving the p(x)-Laplacian

CHINNI', Antonia
2013-01-01

Abstract

We study the existence and multiplicity of weak solutions for a parametric Neumann problem driven by the p(x)-Laplacian. Under a suitable condition on the behavior of the potential at 0^+, we obtain an interval such that when a parameter lambda is in this interval, our problem admits at least one nontrivial weak solution. We show the multiplicity of solutions for potentials satisfying also the Ambrosetti-Rabinowitz condition. Moreover, if the right-hand side f satisfies the Ambrosetti-Rabinowitz condition, then we obtain the existence of two nontrivial weak solutions.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11570/2565168
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