Ground-state nodal solutions for superlinear perturbations of the Robin eigenvalue problem

Abstract

AbstractWe consider a perturbed version of the Robin eigenvalue problem for the p-Laplacian. The perturbation is $$(p - 1)$$ ( p - 1 ) -superlinear. Using the Nehari manifold method, we show that for all parameters $$\lambda < {\hat{\lambda }}_1$$ λ < λ ^ 1 (= the principal eigenvalue of the differential operator), there exists a ground-state nodal solution of the problem.