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A variational proof of a Shilnikov-like theorem. (English) Zbl 0778.34036

The variational approach is used to prove infinitely many solutions of the problem \(x''(t)=-V'(x(t),t,\varepsilon)\), \(x(-\infty)=x(\infty)=0\), where \(\varepsilon\) is a sufficiently small parameter. The obtained criteria are rather effective and can be considered as those in the spirit of the well-known Shilnikov theorem (whence the title).
Reviewer: J.Andres (Olomouc)

MSC:

34C37 Homoclinic and heteroclinic solutions to ordinary differential equations
34C25 Periodic solutions to ordinary differential equations
37-XX Dynamical systems and ergodic theory
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