Electron. J. Diff. Eqns., Vol. 2005(2005), No. 109, pp. 1-12.

Dirichlet problems for semilinear elliptic equations with a fast growth coefficient on unbounded domains

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 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

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

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