Positive solutions for thenonhomogeneous $p$-Laplacianequation in $\mathbb R^N$

Abstract

In this paper, we study a class of nonhomogeneous sublinear-superlinear $p$-Laplacian equations in $\mathbb {R}^N$. By applying a minimization method on the Nehari manifold $\mathcal {N}^{\alpha }$, the existence of positive solutions and the continuity in the perturbation term are obtained.