Existence, Nonexistence, and Multiplicity of Positive Solutions for Nonlocal Boundary Value Problems

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, 2025, vol. 13, issue 5, 1-15

Abstract: This study investigates the nonlocal boundary value problem for generalized Laplacian equations involving a singular, possibly non-integrable weight function. By analyzing the asymptotic behaviors of the nonlinearity f = f ( s ) near both s = 0 and s = ∞ , we establish the existence, nonexistence, and multiplicity of positive solutions for all positive values of the parameter λ . Our proofs employ the fixed-point theorem of cone expansion and compression of norm type, a powerful tool for demonstrating the existence of solutions in cones, as well as the Leray–Schauder fixed-point theorem, which offers an alternative approach for proving the existence of solutions. Illustrative examples are provided to concretely demonstrate the applicability of our main results.

Keywords: generalized Laplacian equations; multiple 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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