Electronic Journal of Differential Equations 15th annual Conference of Applied Mathematics, Univ. of Central Oklahoma,
Electron. J. Diff. Eqns., Conf. 02, 1999, pp. 47-60.

A one dimensional Hammerstein problem

Jun Hua & James L. Moseley

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 November 24, 1999.
Subject Classification: 35P30.
Key words: Hammerstein problem, Nonlinear eigenvalue problem.

Show me the PDF file (138K), TEX file, and other files for this article.

Jun Hua
West Virginia University
Morgantown, West Virginia 26506-6310 USA
James L. Moseley
West Virginia University
Morgantown, West Virginia 26506-6310 USA
e-mail: moseley@math.wvu.edu
Telephone: 304-293-2011

Return to the EJDE web page