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.


58E05 Abstract critical point theory (Morse theory, Lyusternik-Shnirel’man theory, etc.) in infinite-dimensional spaces
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