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arXiv · 2006.16110

A solution to a slightly subcritical elliptic problem with non-power nonlinearity

Monica Clapp·Rosa Pardo·Angela Pistoia·Alberto Saldaña
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Abstract

We consider a slightly subcritical Dirichlet problem with a non-power nonlinearity in a bounded smooth domain. For this problem, standard compact embeddings cannot be used to guarantee the existence of solutions as in the case of power-type nonlinearities. Instead, we use a Ljapunov-Schmidt reduction method to show that there is a positive solution which concentrates at a non-degenerate critical point of the Robin function. This is the first existence result for this type of generalized slightly subcritical problems.

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Monica Clapp, Rosa Pardo, Angela Pistoia, Alberto Saldaña. 2020-06-29. A solution to a slightly subcritical elliptic problem with non-power nonlinearity. https://arxiv.org/abs/2006.16110

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