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

Author

Listed:
  • Jeongmi Jeong

    (Department of mathematics, Pusan National University, Busan 46241, Republic of Korea
    These authors contributed equally to this work.)

  • Chan-Gyun Kim

    (Department of Mathematics Education, Chinju National University of Education, Jinju 52673, Republic of Korea
    These authors contributed equally to this work.)

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.

Suggested Citation

  • 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.
    • Handle: RePEc:gam:jmathe:v:13:y:2025:i:5:p:847-:d:1604606
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