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Subharmonic solutions to second-order differential equations with periodic nonlinearities. (English) Zbl 0985.34033
Here, the authors study the multiplicity of subharmonic solutions to the following equations \[ \ddot u + F_u(t,u) = h(t), \] where \(F\) and \(h\) are periodic in their arguments. Under a nondegenerate condition on the standard action functional associated with the equation, they prove that this equation admits subharmonic solutions of infinitely many levels. Moreover, they also give some results on the existence of true subharmonic solutions. In particular, when \(F(t,u) \equiv G(u)\) or \(F(t,u) = \alpha(t)G(u)\), their results are stronger than those so far known.
Reviewer: Bin Liu (Beijing)

MSC:
34C25 Periodic solutions to ordinary differential equations
58E05 Abstract critical point theory (Morse theory, Lyusternik-Shnirel’man theory, etc.) in infinite-dimensional spaces
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