Super critical problems with concave and convex nonlinearities in ${\mathbb{R}}^N$

Abstract

In this paper, by utilizing a newly established variational principle on convex sets, we provide an existence and multiplicity result for a class of semilinear elliptic problems defined on the whole ${\mathbb{R}}^N$ with nonlinearities involving sublinear and superlinear terms. We shall impose no growth restriction on the nonlinear term and consequently our problem can be super-critical by means of Sobolev spaces.

arXiv admin note: text overlap with arXiv:1706.08385