Positive solutions of elliptic systems with superlinear terms on the critical hyperbola
Analysis of PDEs
2023-11-20 v1
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.
Keywords
Cite
@article{arxiv.2311.10355,
title = {Positive solutions of elliptic systems with superlinear terms on the critical hyperbola},
author = {Mabel Cuesta and Rosa Pardo and Angela Pistoia},
journal= {arXiv preprint arXiv:2311.10355},
year = {2023}
}