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Zbl 1203.34067
Lv, Xiang; Lu, Shiping; Yan, Ping
Homoclinic solutions for nonautonomous second-order Hamiltonian systems with a coercive potential. (English)
[J] Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 72, No. 7-8, 3484-3490 (2010). ISSN 0362-546X

Let $F\in C^1(R\times R^n,R)$ be a $T$-periodic function with respect to $t$ ($T>0$), $f: R \to R^n$ be a continuous and bounded function. The second-order Hamiltonian system $$\ddot{u}(t)=\nabla(F(t,u(t)))+f(t)$$ is considered. Using more general conditions on the right-hand side than other researches, the authors prove the existence of homoclinic orbits for such systems.
[Sergei Kornev (Voronezh)]

MSC 2000:: *34C37 Homoclinic and heteroclinic solutions of ODE
37J45 Periodic, homoclinic and heteroclinic orbits, etc.

Keywords: Hamiltonian system; homoclinic orbits; coercive potential

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