Existence Solutions for a Singular Nonlinear Problem with Dirichlet Boundary Conditions on Exterior Domains | ||
| Kirkuk Journal of Science | ||
| Article 1, Volume 19, Issue 1, March 2024, Pages 1-15 PDF (313.93 K) | ||
| Document Type: Research Paper | ||
| DOI: 10.32894/kujss.2024.144848.1122 | ||
| Authors | ||
| Mageed Ali* 1; Joseph Iaia2 | ||
| 1Mathematics Department, College of Science, Kirkuk University, Kirkuk, Iraq. | ||
| 2Mathematics Department, College of Science, University of North Texas, Denton, USA. | ||
| Abstract | ||
| This paper proves the existence of solutions that solve the Nonlinear Partial differential equation on the exterior of the ball centered at the origin in R^{N} with radius R > 0, with boundary conditions u = 0 on the boundary, and u ( x ) approaches 0 as | x | approaches infinity. When the function is local Lipschitzian grows superlinear at infinity and singular at 0. Also N > 2, f ( u ) ~ (-1 ) / ( |u| ^{q-1} u ) for small u with 0 < q < 1, and f ( u ) ~ | u |^{ p-1} u for large | u | with p > 1. Also, K ( x ) ~ | x |^ { - ( Alpha) } with 2 < Alpha < 2 ( N - 1 ) for large | x |. We used the fixed point method and other techniques to prove the existence. | ||
| Keywords | ||
| exterior domains; singular; Nonlinear; existence | ||
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