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

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.