Electronic Journal of Differential Equations,
Conference 02 (1999), pp. 47-60.

Title: A one dimensional Hammerstein problem

Authors: Jun Hua (West Virginia Univ., Morgantown, WV, USA)
James L. Moseley (West Virginia Univ., Morgantown, WV, USA)
 
Abstract: 
Nonlinear equations of the form $L[u]=\lambda g(u)$ where $L$ is a linear
operator on a function space and $g$ maps $u$ to the composition function
$g\circ u$ 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 $B[u]=\lambda L^{-1}[g(u)]$. To investigate the importance of
the growth rate of $g$ and the sign and magnitude of $\lambda $ on the
number of solutions of such problems, in this paper we consider the
one-dimensional problem $L(x)=\lambda g(x)$ where $L(x)=ax$.


Published December 9, 1999.
Math Subject Classifications: 35P30.
Key Words: Hammerstein problem; nonlinear eigenvalue problem.