A sub-super solution method to continuous weak solutions for a semilinear elliptic boundary value problems on bounded and unbounded domains

Abdeljabbar Ghanmi; Hadeel Z. Alzumi; Noureddine Zeddini; Abdeljabbar Ghanmi; Hadeel Z. Alzumi; Noureddine Zeddini

doi:10.3934/era.2024170

Electronic Research Archive

2024, Volume 32, Issue 6: 3742-3757. doi: 10.3934/era.2024170

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A sub-super solution method to continuous weak solutions for a semilinear elliptic boundary value problems on bounded and unbounded domains

1.
Department of Mathematics and Statistics, Faculty of Science, University of Jeddah, Jeddah 21493, Saudi Arabia
2.
Department of Mathematics, College of Science, Taibah University, Madinah, KSA

Received: 26 March 2024 Revised: 15 May 2024 Accepted: 31 May 2024 Published: 07 June 2024

In this paper, we prove the existence of solutions for an elliptic system. More precisely, we combine the potential theory with the sub-super solution method and use the properties of the well-known Kato class to justify our existence results. The novelty of our study is that we consider either the bounded or the exterior domain; Also, the nonlinearities may be singular near the boundary. Some examples are presented to validate our main results.
- Green's function,
- elliptic systems,
- Schauder fixed point theorem,
- sub-supersolutions method
Citation: Abdeljabbar Ghanmi, Hadeel Z. Alzumi, Noureddine Zeddini. A sub-super solution method to continuous weak solutions for a semilinear elliptic boundary value problems on bounded and unbounded domains[J]. Electronic Research Archive, 2024, 32(6): 3742-3757. doi: 10.3934/era.2024170

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Abstract

In this paper, we prove the existence of solutions for an elliptic system. More precisely, we combine the potential theory with the sub-super solution method and use the properties of the well-known Kato class to justify our existence results. The novelty of our study is that we consider either the bounded or the exterior domain; Also, the nonlinearities may be singular near the boundary. Some examples are presented to validate our main results.

References

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