Positive Solutions of Elliptic Systems with Superlinear Terms on the Critical Hyperbola - Archive ouverte HAL
Article Dans Une Revue Milan Journal of Mathematics Année : 2024

Positive Solutions of Elliptic Systems with Superlinear Terms on the Critical Hyperbola

Résumé

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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Dates et versions

hal-04698164 , version 1 (15-09-2024)

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Mabel Cuesta, Angela Pistoia, Rosa Pardo. Positive Solutions of Elliptic Systems with Superlinear Terms on the Critical Hyperbola. Milan Journal of Mathematics, 2024, ⟨10.1007/s00032-024-00401-z⟩. ⟨hal-04698164⟩
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