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Existence of Positive Solutions to Singular Boundary Value Problems Involving φ -Laplacian

Author

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  • Jeongmi Jeong

    (Department of Mathematics, Pusan National University, Busan 609-735, Korea
    These authors contributed equally to this work.)

  • Chan-Gyun Kim

    (Department of Mathematics Education, Pusan National University, Busan 609-735, Korea
    These authors contributed equally to this work.)

Abstract

This paper is concerned with the existence of positive solutions to singular Dirichlet boundary value problems involving φ -Laplacian. For non-negative nonlinearity f = f ( t , s ) satisfying f ( t , 0 ) ≢ 0 , the existence of an unbounded solution component is shown. By investigating the shape of the component depending on the behavior of f at ∞ , the existence, nonexistence and multiplicity of positive solutions are studied.

Suggested Citation

  • 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.
    • Handle: RePEc:gam:jmathe:v:7:y:2019:i:7:p:654-:d:250367
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    Cited by:

    1. 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.
    2. Jeongmi Jeong & Chan-Gyun Kim, 2025. "Existence, Nonexistence, and Multiplicity of Positive Solutions for Nonlocal Boundary Value Problems," Mathematics, MDPI, vol. 13(5), pages 1-15, March.
    3. Chan-Gyun Kim, 2020. "Existence and Multiplicity Results for Nonlocal Boundary Value Problems with Strong Singularity," Mathematics, MDPI, vol. 8(5), pages 1-25, May.
    4. Jeongmi Jeong & Chan-Gyun Kim, 2020. "Existence of Positive Solutions to Singular φ -Laplacian Nonlocal Boundary Value Problems when φ is a Sup-multiplicative-like Function," Mathematics, MDPI, vol. 8(3), pages 1-18, March.

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