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

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https://doi.org/10.1016/j.jde.2020.11.030
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2020-12-22
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Elsevier
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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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Análisis matemático
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1202 Análisis y Análisis Funcional
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https://hdl.handle.net/20.500.14352/7279
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