Supercritical problems with concave and convex nonlinearities in ℝN

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 [Formula: see text] with nonlinearities involving linear and superlinear terms. We shall impose no growth restriction on the nonlinear term, and consequently, our problem can be supercritical in the sense of the Sobolev embeddings.