Supercritical problems with concave and convex nonlinearities in \(\mathbb{R}^N\). (English) Zbl 1472.35192
Summary: 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 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.
MSC:
| 35J91 | Semilinear elliptic equations with Laplacian, bi-Laplacian or poly-Laplacian |
| 35A01 | Existence problems for PDEs: global existence, local existence, non-existence |
| 35J20 | Variational methods for second-order elliptic equations |
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