## Existence and multiplicity results for homogeneous second order differential equations.(English)Zbl 0808.58013

This paper uses constrained critical point theory and Szulkin’s version of Lyusternik-Schnirelman theory to extend some results of Lassoued on the existence of infinitely many pairs of distinct nonconstant periodic solutions for some second order differential systems of the form $-u'' + \nabla_ u V(t,u) = 0.$ Some results are also proved for the Neumann problem associated to a semilinear elliptic equation. They all depend on some abstract critical point theorem also given in the paper.

### MSC:

 5.8e+06 Abstract critical point theory (Morse theory, Lyusternik-Shnirel’man theory, etc.) in infinite-dimensional spaces

### Keywords:

minimax theorems; Hamiltonian systems
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