97-544 Benguria, R., Depassier, M.C.

Variational Method for Nonlinear Eigenvalue Problems (511K, ps file) Oct 15, 97

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Abstract. We present a new variational technique to characterize eigenvalues of several nonlinear problems. We apply it in detail to two different problems described by nonlinear ODE's. First we consider the bifurcation problem $u''+\lambda u= N(u)$ with two point boundary conditions where $N(u)$ is a general nonlinear term, and give a variational characterization for the eigenvalue $\lambda$. The second problem is the determination of the asymptotic speed, $c$, of propagation of fronts for the one dimensional reaction--diffusion equation $u_t=u_{xx}+f(u)$. We will obtain a variational characterization of $c$ for different types of reaction terms $f(u)$. An extension to nonlinear eigenvalue problems described by PDE's will be briefly described.

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