Electron. J. Diff. Equ., Vol. 2013 (2013), No. 95, pp. 1-14.

Asymptotic behavior of positive solutions of a semilinear Dirichlet problem outside the unit ball

Habib Maagli, Sameh Turki, Zagharide Zine El Abidine

Abstract:
In this article, we are concerned with the existence, uniqueness and asymptotic behavior of a positive classical solution to the semilinear boundary-value problem
$$\displaylines{ -\Delta u=a(x)u^{\sigma }\quad\hbox{in }D, \cr \lim _{|x|\to 1}u(x)= \lim_{|x|\to \infty}u(x) =0. }$$
Here D is the complement of the closed unit ball of $\mathbb{R} ^n$ ( $n\geq 3$), $\sigma<1$ and the function a is a nonnegative function in $C_{loc}^{\gamma}(D)$, $0<\gamma<1$, satisfying some appropriate assumptions related to Karamata regular variation theory.

Submitted February 7, 2013. Published April 11, 2013.
Math Subject Classifications: 31C35, 34B16, 60J50.
Key Words: Asymptotic behavior; Dirichlet problem; subsolution; supersolution.

Show me the PDF file (272 KB), TEX file, and other files for this article.

Habib Mâagli
King Abdulaziz University, College of Sciences and Arts
Rabigh Campus, Department of Mathematics
P. O. Box 344, Rabigh 21911, Saudi Arabia
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
Zagharide Zine El Abidine
Département de Mathématiques, Faculté des Sciences de Tunis
Campus Universitaire, 2092 Tunis, Tunisia
email: Zagharide.Zinelabidine@ipeib.rnu.tn

Return to the EJDE web page