Electronic Journal of Differential Equations (Jul 2001)

A two dimensional Hammerstein problem: The linear case

  • Jun Hua,
  • James L. Moseley

Journal volume & issue
Vol. Conference, no. 07
pp. 71 – 88

Abstract

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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 $gcirc u$ 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.

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