 97544 Benguria, R., Depassier, M.C.
 Variational Method for Nonlinear Eigenvalue Problems
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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 reactiondiffusion
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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