We study the existence and multiplicity of solutions for a parametric equation driven by the p-laplacian operator on unbounded intervals. Precisely, by using a recent local minimum theorem we prove the existence of a nontrivial nonnegative solution to an equation in the real line, without assuming any asymptotic condition neither at zero nor infinity on the nonlinear term. As a special case, we note the existence of a nontrivial solution for the problem when the nonlinear term is sublinear at zero. Moreover, under a suitable superlinear growth at infinity on the nonlinearity we prove a multiplicity result for such a problem.

A variational approach to multiplicity results for boundary value problems on the real line

BARLETTA, Giuseppina;
2015-01-01

Abstract

We study the existence and multiplicity of solutions for a parametric equation driven by the p-laplacian operator on unbounded intervals. Precisely, by using a recent local minimum theorem we prove the existence of a nontrivial nonnegative solution to an equation in the real line, without assuming any asymptotic condition neither at zero nor infinity on the nonlinear term. As a special case, we note the existence of a nontrivial solution for the problem when the nonlinear term is sublinear at zero. Moreover, under a suitable superlinear growth at infinity on the nonlinearity we prove a multiplicity result for such a problem.
2015
Unbounded domains; boundary value problem; critical points
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/20.500.12318/6220
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