Positive solutions of elliptic systems with superlinear terms on the critical hyperbola

Mabel Cuesta; Rosa Pardo; Angela Pistoia

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arXiv · 2311.10355

Positive solutions of elliptic systems with superlinear terms on the critical hyperbola

Mabel Cuesta·Rosa Pardo·Angela Pistoia

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Abstract

We consider a slightly subcritical elliptic system with Dirichlet boundary conditions and 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 the dual method on Orlicz spaces, showing that our problem possesses a mountain pass type solution.

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Mabel Cuesta, Rosa Pardo, Angela Pistoia. 2023-11-17. Positive solutions of elliptic systems with superlinear terms on the critical hyperbola. https://arxiv.org/abs/2311.10355

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