Existence result for a system of two semilinear coupled Poisson equations with asymptotically linear nonlinearities

Ablanvi Songo

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arXiv · 2509.22899

Existence result for a system of two semilinear coupled Poisson equations with asymptotically linear nonlinearities

Ablanvi Songo

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Abstract

We establish the existence of at least one solution to a system of two semilinear coupled Poisson equations with asymptotically linear nonlinearities, without imposing the Ambrosetti-Rabinowitz condition or any of its refinements. The proof relies on a generalized saddle point theorem due to Colin and the author \cite{CS}.

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Ablanvi Songo. 2025-09-26. Existence result for a system of two semilinear coupled Poisson equations with asymptotically linear nonlinearities. https://arxiv.org/abs/2509.22899

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