IJPAM: Volume 4, No. 3 (2003)

EXISTENCES, ASYMPTOTIC BEHAVIORS AND
SYMMETRIC PROPERTIES OF SOLUTIONS OF
SEMILINEAR ELLIPTIC EQUATIONS IN
FLAT FLASK DOMAINS

Huei-Li Lin, Hwai-Chiuan Wang$^1$
Department of Mathematics
National Tsing Hua University
Hsinchu, Taiwan 30013, R.O.C.
$^1$e-mail: hwang@mail.math.hthv.edu.tw


Abstract.We assert that there exists a ground state solution of equation ([*]) in a flat flask domain: the Esteban-Lions domain $\mathbb{S}_{0}^{r}$ by adding an arbitrary small width but sufficient long corridor. We also establish the asymptotic behavior and the symmetry of solutions of equation ([*]) in flat flask domains.

Received: December 5, 2002

AMS Subject Classification: 35J20, 35J25

Key Words and Phrases: semilinear elliptic equation, asymptotic behavior, symmetry, flat flask domain

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2003
Volume: 4
Issue: 3