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Zbl 0669.34035
Tanaka, Kazunaga
Morse indices at critical points related to the symmetric mountain pass theorem and applications. (English)
[J] Commun. Partial Differ. Equations 14, No.1, 99-128 (1989). ISSN 0360-5302; ISSN 1532-4133/e

The author obtains estimates of Morse indices of an even functional $I\in C(E,R)$ at critical points related to the symmetric mountain pass theorem. As application, he deals with the existence of multiple solutions of inhomogeneous superlinear boundary value problems. He also deals with the superlinear Sturm-Liouville problem: $-u''=g(u)$ in (0,1), $u(0)=u(1)=0$, and he gives a complete characterization of the solutions related to the symmetric mountain pass theorem.
[Zhang Di]

MSC 2000:: *34C05 Qualitative theory of some special solutions of ODE
34L99 Ordinary differential operators
34B05 Linear boundary value problems of ODE

Keywords: Morse indices; symmetric mountain pass theorem; inhomogeneous superlinear boundary value problems; superlinear Sturm-Liouville problem

Cited in: Zbl 1017.31002

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