Electron. J. Diff. Eqns., Vol. 2003(2003), No. 49, pp. 1-16.

Existence of positive solutions for Dirichlet problems of some singular elliptic equations

Zhiren Jin

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 similar to the singular Emden-Fowler equation. The proof is based on a super and sub-solution method. A super solution is constructed by Perron's method together with a family of auxiliary functions.

Submitted December 11, 2002. Published April 29, 2003.
Math Subject Classifications: 35J25, 35J60, 35J65.
Key Words: Elliptic boundary value problems, positive solutions, singular semilinear equations, unbounded domains, Perron's method, super solutions.

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Zhiren Jin
Department of Mathematics and Statistics
Wichita State University
Wichita, Kansas, 67260-0033, USA
email: zhiren@math.twsu.edu

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