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Morse indices at critical points related to the symmetric mountain pass theorem and applications. (English) Zbl 0669.34035
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.
Reviewer: Zhang Di

MSC:
34C05 Topological structure of integral curves, singular points, limit cycles of ordinary differential equations
34L99 Ordinary differential operators
34B05 Linear boundary value problems for ordinary differential equations
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