When an unbounded domain is inside a slab, existence of a positive solution is proved for the Dirichlet problem of a class of semilinear elliptic equations that are similar either to the singular Emden-Fowler equation or a sublinear elliptic equation. The result obtained can be applied to equations with coefficients of the nonlinear term growing exponentially. The proof is based on the super and sub-solution method. A super solution itself is constructed by solving a quasilinear elliptic equation via a modified Perron's method.
Submitted February 11, 2005. Published October 10, 2005.
Math Subject Classifications: 35J25, 35J60, 35J65.
Key Words: Elliptic boundary-value problems; positive solutions; semilinear equations; unbounded domains; Perron's method; super solutions
Show me the PDF file (245K), TEX file, and other files for this article.
| Zhiren Jin |
Department of Mathematics and Statistics
Wichita State University
Wichita, Kansas, 67260-0033, USA
Return to the EJDE web page