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Ljusternik-Schnirelman theory on general level sets. (English) Zbl 0608.58014
This paper is devoted to the nonlinear eigenvalue problem \(\mu\) \(a'(u)=b'(u)\) when a’ and b’ are both indefinite. The author obtains existence theorems and, when a and b are even, multiplicity results. The basic idea is to use deformations on the level sets \(N_{\alpha}=\{u:\) \(b(u)=\alpha \}\) and a minimax principle. Applications are given to abstract Hammerstein equations, Hammerstein integral equations and nonlinear elliptic equations.
Reviewer: M.Willem

MSC:
58E05 Abstract critical point theory (Morse theory, Lyusternik-Shnirel’man theory, etc.) in infinite-dimensional spaces
58J32 Boundary value problems on manifolds
45G10 Other nonlinear integral equations
45N05 Abstract integral equations, integral equations in abstract spaces
35J65 Nonlinear boundary value problems for linear elliptic equations
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