Eun Kyoung Lee, Inbo Sim, Byungjae Son
Abstract:
We investigate the existence, multiplicity and nonexistence of positive solutions to
nonlinear (singular) elliptic problems involving nonhomogeneous operators and mixed
nonlocal boundary conditions based on the behaviors of the nonlinear term near \(0\)
and \(\infty\). In particular, we discuss the existence of at least three positive
solutions to the mixed nonlocal boundary problems, which is new finding even for
the problems involving homogeneous operators. The novelty of this study lies in
constructing completely continuous operators related to nonlinear elliptic problems
involving complicated boundary conditions. We emphasize that only one fixed point
theorem is used to obtain the existence and multiplicity results, despite generalizing
and extending most of the problems in previous literature.
Submitted February 20, 2025. Published June 30, 2025.
Math Subject Classifications: 34B10, 34B16, 34B18.
Key Words: Singular elliptic problem; nonhomogeneous operator; integral boundary condition; multipoint boundary condition; positive solution.
DOI: 10.58997/ejde.2025.66
Show me the PDF file (377 KB), TEX file for this article.
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Eun Kyoung Lee Department of Mathematics Education Pusan National University Busan 46241, Republic of Korea email: eklee@pusan.ac.kr |
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Inbo Sim Department of Mathematics University of Ulsan Ulsan 44610, Republic of Korea email: ibsim@ulsan.ac.kr |
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Byungjae Son School of Science, Technology, and Mathematics Ohio Northern University, OH 45810, USA email: b-son@onu.edu |
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