Solutions to the nonautonomous bistable equation with specified Morse index. I. Existence

Alikakos, Nicholas D.; Bates, Peter W.; Fusco, Giorgio

doi:10.1090/S0002-9947-1993-1167183-0

Solutions to the nonautonomous bistable equation with specified Morse index. I. Existence
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by Nicholas D. Alikakos, Peter W. Bates and Giorgio Fusco PDF

Trans. Amer. Math. Soc. 340 (1993), 641-654 Request permission

Abstract:

We investigate the existence of unstable solutions of specified Morse index for the equation ${\varepsilon ^2}{u_{xx}} - f(x,u) = 0$ on a finite interval and Neumann boundary conditions.

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