## 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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### References:

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