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 ℝN 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.

中文翻译：

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ℝN 中具有凹凸非线性的超临界问题

本文利用新建立的凸集变分原理，给出了一类整体上定义的半线性椭圆问题的存在性和多重性结果。ℝñ具有涉及线性和超线性项的非线性。我们不会对非线性项施加增长限制，因此，我们的问题在 Sobolev 嵌入的意义上可能是超临界的。