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Mathematics
Volume 13
Issue 20
10.3390/math13203322
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Article

Existence of Positive Solutions for a System of Generalized Laplacian Problems

by
Chan-Gyun Kim
Department of Mathematics Education, Chinju National Univeristy of Education, Jinju 52673, Republic of Korea
Mathematics 2025, 13(20), 3322; https://doi.org/10.3390/math13203322
Submission received: 28 August 2025 / Revised: 10 October 2025 / Accepted: 16 October 2025 / Published: 17 October 2025
Versions Notes

Abstract

This paper investigates the existence and multiplicity of positive solutions for a system of generalized Laplacian problems. By analyzing the asymptotic behavior of 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 ∞.
Keywords: generalized Laplacian system; positive solutions; singular weight function generalized Laplacian system; positive solutions; singular weight function

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MDPI and ACS Style

Kim, C.-G. Existence of Positive Solutions for a System of Generalized Laplacian Problems. Mathematics 2025, 13, 3322. https://doi.org/10.3390/math13203322

AMA Style

Kim C-G. Existence of Positive Solutions for a System of Generalized Laplacian Problems. Mathematics. 2025; 13(20):3322. https://doi.org/10.3390/math13203322

Chicago/Turabian Style

Kim, Chan-Gyun. 2025. "Existence of Positive Solutions for a System of Generalized Laplacian Problems" Mathematics 13, no. 20: 3322. https://doi.org/10.3390/math13203322

APA Style

Kim, C.-G. (2025). Existence of Positive Solutions for a System of Generalized Laplacian Problems. Mathematics, 13(20), 3322. https://doi.org/10.3390/math13203322

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