16th Conference on Applied Mathematics, Univ. of Central Oklahoma,
Electron. J. Diff. Eqns., Conf. 07, 2001, pp. 7188.
A two dimensional Hammerstein problem: The linear case
Jun Hua & James L. Moseley
Abstract:
Nonlinear equations of the form
where
is a linear operator on a function space and
maps
to the composition function
arise in the theory of spontaneous combustion. We assume
is invertible so that such an equation can be written as a Hammerstein
equation,
where
.
To investigate the importance of the growth rate of
and the sign and magnitude of
on the number of solutions of such problems, in a previous paper we
considered the onedimensional problem
where
.
This paper extends these results to two dimensions for the linear case.
Published July 20, 2001.
Subject lassfications: 47H30.
Key words: Hammerstein problem, nonlinear differential equation.
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Jun Hua
West Virginia University
Morgantown, West Virginia 265066310 USA 

James L. Moseley
West Virginia University
Morgantown, West Virginia 265066310 USA
email: moseley@math.wvu.edu
Telephone: 3042932011 
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