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.