Solutions to nonlinear elliptic problems with nonhomogeneous operators and mixed nonlocal boundary conditions
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 exis...
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| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
Texas State University
2025-06-01
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| Series: | Electronic Journal of Differential Equations |
| Subjects: | |
| Online Access: | http://ejde.math.txstate.edu/Volumes/2025/66/abstr.html |
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| Summary: | 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. |
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| ISSN: | 1072-6691 |