Opuscula Math. 42, no. 6 (2022), 793-803
https://doi.org/10.7494/OpMath.2022.42.6.793
Opuscula Mathematica
Nonnegative solutions for a class of semipositone nonlinear elliptic equations in bounded domains of Rn
Imed Bachar
Habib Mâagli
Hassan Eltayeb
Abstract. In this paper, we obtain sufficient conditions for the existence of a unique nonnegative continuous solution of semipositone semilinear elliptic problem in bounded domains of \(\mathbb{R}^n\) (\(n\geq 2\)). The global behavior of this solution is also given.
Keywords: nonnegative solution, semipositone, Kato class, fixed point theorem.
Mathematics Subject Classification: 35J25, 35A01, 35B09, 35J08.
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- Imed Bachar (corresponding author)
https://orcid.org/0000-0003-3808-5786- King Saud University, College of Science, Mathematics Department, P.O. Box 2455, Riyadh 11451, Saudi Arabia
- Habib Mâagli
- https://orcid.org/0000-0002-7977-8039
- King Abdulaziz University, College of Sciences and Arts, Rabigh Campus, Department of Mathematics, P.O. Box 344, Rabigh 21911, Saudi Arabia
- Hassan Eltayeb
- https://orcid.org/0000-0003-1820-9921
- King Saud University, College of Science, Mathematics Department, P.O. Box 2455, Riyadh 11451, Saudi Arabia
- Communicated by Vicentiu D. Rădulescu.
- Received: 2022-05-26.
- Revised: 2022-09-18.
- Accepted: 2022-09-19.
- Published online: 2022-11-24.
