Positive Solutions for a Singular Nonlinear Problem on a Bounded Domain in R 2 |
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Authors: | Zeddini Noureddine |
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Institution: | (1) Département de Mathématiques, Faculté des Sciences de Tunis, Campus Universitaire, 1060 Tunis, Tunisia |
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Abstract: | For a bounded regular Jordan domain in R
2, we introduce and study a new class of functions K( ) related on its Green function G. We exploit the properties of this class to prove the existence and the uniqueness of a positive solution for the singular nonlinear elliptic equation u+ (x,u)=0, in D ( ), with u=0 on ![part](/content/q4k1j478h2x0847t/xxlarge8706.gif) and u C ( ), where is a nonnegative Borel measurable function in ×(0, ) that belongs to a convex cone which contains, in particular, all functions (x,t)=q(x)t
– , >0 with nonnegative functions q K( ). Some estimates on the solution are also given. |
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Keywords: | singular elliptic equation Green function Schauder fixed point theorem Maximum principle Superharmonic function |
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