%0 Journal Article
%T Existence Solutions for a Singular Nonlinear Problem with Dirichlet Boundary Conditions on Exterior Domains
%J Kirkuk Journal of Science
%I University of Kirkuk
%Z 3005-4788
%A Ali, Mageed
%A Iaia, Joseph
%D 2024
%\ 03/01/2024
%V 19
%N 1
%P 1-15
%! Existence Solutions for a Singular Nonlinear Problem with Dirichlet Boundary Conditions on Exterior Domains
%K exterior domains
%K Singular
%K nonlinear
%K existence
%R 10.32894/kujss.2024.144848.1122
%X 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.
%U https://kujss.uokirkuk.edu.iq/article_182462_443723c2dfe8b460ca60cf3a21b20a96.pdf