Existence, Nonexistence and Multiplicity of Positive Solutions for Generalized Laplacian Problems with a Parameter

Jeongmi Jeong and Chan-Gyun Kim ()
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Jeongmi Jeong: Department of Mathematics, Pusan National University, Busan 46241, Republic of Korea
Chan-Gyun Kim: Department of Mathematics Education, Chinju National University of Education, Jinju 52673, Republic of Korea

Mathematics, 2024, vol. 12, issue 23, 1-11

Abstract: We investigate the homogeneous Dirichlet boundary value problem for generalized Laplacian equations with a singular, potentially non-integrable weight. By examining asymptotic behaviors of the nonlinear term near 0 and ∞ , we establish the existence, nonexistence, and multiplicity of positive solutions for all positive values of the parameter λ . Our proofs rely on the fixed point theorem concerning cone expansion and compression of norm type and the Leray–Schauder’s fixed point theorem.

Keywords: generalized Laplacian problems; multiplicity of positive solutions; singular weight function (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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