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.

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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

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