Jun Hua & James L. Moseley
Abstract:
Nonlinear equations of the form
![$L[u]=\lambda g(u)$](gifs/aa.gif)
where L is a linear
operator on a function space and g maps u to the composition
function
arise
in the theory of spontaneous combustion. If L is
invertible, such an equation can be written as a Hammerstein equation,
u=B[u] where
![$B[u]=\lambda L^{-1}[g(u)]$](gifs/ac.gif)
. To investigate the importance of
the growth rate of g and the sign and magnitude of
on the
number of solutions of such problems, in this paper we consider the
one-dimensional problem
where L(x)=ax.
Published November 24, 1999.
Subject Classification: 35P30.
Key words: Hammerstein problem, Nonlinear eigenvalue problem.
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Jun Hua West Virginia University Morgantown, West Virginia 26506-6310 USA |
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James L. Moseley West Virginia University Morgantown, West Virginia 26506-6310 USA e-mail: moseley@math.wvu.edu Telephone: 304-293-2011 |
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