Electronic Journal of Differential Equations,
Conference 07 (2001), pp. 71-88.

Title: A two dimensional Hammerstein problem The linear case.

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. We assume $L$ is
 invertible so that 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 a previous paper we
 considered the one-dimensional problem $L(x)=\lambda g(x)$ where $L(x)=ax$.
 This paper extends these results to two dimensions for the linear case.

Published July 20, 2001.
Math Subject Classifications: 47H30.
Key Words: Hammerstein problem; nonlinear differential equation.