Electron. J. Diff. Equ., Vol. 2009(2009), No. 108, pp. 1-6.

Positive solutions for semi-linear elliptic equations in exterior domains

Habib Maagli, Sameh Turki, Noureddine Zeddini

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.

Show me the PDF file (198 KB), TEX file, and other files for this article.

Habib Maagli
Département de Mathématiques, Faculté des Sciences de Tunis
Campus Universitaire, 2092 Tunis, Tunisia
email: habib.maagli@fst.rnu.tn
Sameh Turki
Département de Mathématiques, Faculté des Sciences de Tunis
Campus Universitaire, 2092 Tunis, Tunisia
email: sameh.turki@ipein.rnu.tn
Noureddine Zeddini
Département de Mathématiques, Faculté des Sciences de Tunis
Campus Universitaire, 2092 Tunis, Tunisia
email: noureddine.zeddini@ipein.rnu.tn

Return to the EJDE web page