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

Q: What type of study is this?

This is a Quantitative Study study.

Ablanvi Songo

doi:10.48550/arxiv.2509.22899

September 26, 2025Open Access

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

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Key Points

At least one solution exists for the system of two coupled Poisson equations without specific conditions.
The proof uses a generalized saddle point theorem, which extends existing methodologies in the field.
This research presents a novel approach to proving existence results without relying on conventional conditions.
Findings may influence future studies involving coupled partial differential equations across various applications.

Implication

Research demonstrates existence of solutions for coupled Poisson equations, avoiding Ambrosetti-Rabinowitz condition.

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 {CS}.

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Cite This Study

Ablanvi Songo (2025) studied this question.

synapsesocial.com/papers/68f6196ee0bbbc94fac36467 https://doi.org/10.48550/arxiv.2509.22899

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

Key Points

Implication

Abstract

Discussion

Cite This Study

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

Key Points

Implication

Abstract

Discussion

Cite This Study

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