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September 5, 2025Open Access

Existence of Positive Solutions for a System of Generalized Laplacian Problems

Key Points

The study shows the existence and multiplicity of positive solutions under certain conditions.
Key findings indicate that the norm of positive solutions behaves predictably as the parameter λ approaches extremes.
Observational analysis of the asymptotic behavior of nonlinearity aided in establishing conditions for solutions.
The results highlight the significance of norm behavior as a crucial factor in understanding solution existence.

Abstract

This paper investigates the existence and multiplicity of positive solutions for a system of generalized Laplacian problems. By analyzing the asymptotic behavior of the nonlinearity, we establish conditions for the existence of positive solutions and the presence of multiple positive solutions. Our main results reveal how the norm of the positive solutions behaves as the parameter λ approaches 0 or ∞, specifically that the norm tends to either 0 or ∞.

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Chan-Gyun Kim (Mon,) studied this question.

synapsesocial.com/papers/68bb4def6d6d5674bcd01f45 https://doi.org/https://doi.org/10.20944/preprints202508.2208.v1

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