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.
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