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Homoclinic solutions for nonautonomous second-order Hamiltonian systems with a coercive potential. (English) Zbl 1203.34067
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.

MSC:
34C37Homoclinic and heteroclinic solutions of ODE
37J45Periodic, homoclinic and heteroclinic orbits; variational methods, degree-theoretic methods
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References:
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