Existence of Positive Solutions for a System of Generalized Laplacian Problems

Chan-Gyun Kim ()
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Chan-Gyun Kim: Department of Mathematics Education, Chinju National Univeristy of Education, Jinju 52673, Republic of Korea

Mathematics, 2025, vol. 13, issue 20, 1-13

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 (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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