Electronic Journal of Differential Equations,
Vol. 2009(2009), No. 108, pp. 1-6.

Title: Positive solutions for semi-linear elliptic
       equations in exterior domains

Authors: Habib Maagli (Campus Univ., Tunis, Tunisia)
         Sameh Turki  (Campus Univ., Tunis, Tunisia)
	 Noureddine Zeddini (Campus Univ., Tunis, Tunisia)

Abstract: 
 We prove the existence of a solution, decaying to zero at
 infinity, for the  second order differential
 equation
 $$
 \frac{1}{A(t)}(A(t)u'(t))'+\phi(t)+f(t,u(t))=0,\quad t\in (a,\infty).
 $$
 Then we give a simple proof, under some sufficient conditions which
 unify and generalize most of those given in the bibliography,  for
 the existence of a positive solution for the semilinear second order
 elliptic equation
 $$
 \Delta u+\varphi(x,u)+g( |x|) x.\nabla u =0,
 $$
 in an exterior domain of the Euclidean space ${\mathbb{R}}^{n},n\geq 3$.
 
Submitted August 12, 2009. Published September 10, 2009.
Math Subject Classifications: 34A12, 35J60.
Key Words: Positive solutions; nonlinear elliptic equations; exterior domain.