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

Author

Listed:
  • 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)

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.

Suggested Citation

  • Jeongmi Jeong & Chan-Gyun Kim, 2024. "Existence, Nonexistence and Multiplicity of Positive Solutions for Generalized Laplacian Problems with a Parameter," Mathematics, MDPI, vol. 12(23), pages 1-11, November.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:23:p:3668-:d:1527441
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    References listed on IDEAS

    as
    1. Jeongmi Jeong & Chan-Gyun Kim, 2019. "Existence of Positive Solutions to Singular Boundary Value Problems Involving φ -Laplacian," Mathematics, MDPI, vol. 7(7), pages 1-13, July.
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