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

2023/11/17 by Mabel Cuesta, Cuesta, Mabel, Rosa Pardo San Gil +3
Mathematics · Computer Science · #Nonlinear Partial Differential Equations #Advanced Mathematical Modeling in Engineering #Advanced Mathematical Physics Problems

paper · pdf · doi:10.48550/arxiv.2311.10355

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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