Electron. J. Diff. Eqns.,
Vol. 2005(2005), No. 109, pp. 112.
Dirichlet problems for semilinear elliptic equations
with a fast growth coefficient on unbounded domains
Zhiren Jin
Abstract:
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 EmdenFowler 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 subsolution 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 boundaryvalue 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, 672600033, USA
email: zhiren@math.wichita.edu 
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