TY - JOUR
ID - 182462
TI - Existence Solutions for a Singular Nonlinear Problem with Dirichlet Boundary Conditions on Exterior Domains
JO - Kirkuk Journal of Science
JA - KUJSS
LA - en
SN - 3005-4788
AU - Ali, Mageed
AU - Iaia, Joseph
AD - Mathematics Department, College of Science, Kirkuk University, Kirkuk, Iraq.
AD - Mathematics Department, College of Science, University of North Texas, Denton, USA.
Y1 - 2024
PY - 2024
VL - 19
IS - 1
SP - 1
EP - 15
KW - exterior domains
KW - Singular
KW - nonlinear
KW - existence
DO - 10.32894/kujss.2024.144848.1122
N2 - 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.
UR - https://kujss.uokirkuk.edu.iq/article_182462.html
L1 - https://kujss.uokirkuk.edu.iq/article_182462_443723c2dfe8b460ca60cf3a21b20a96.pdf
ER -