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Existence of homoclinic solutions for a class of second-order Hamiltonian systems. (English) Zbl 1186.34059
Summary: Consider the second-order nonautonomous Hamiltonian systems $$\ddot u(t)-L(t)u(t)+\nabla W(t,u(t))=0$$ where $t\in R$, $u\in R^n$, $L\in C(R,R^{n\times n})$ is a symmetric matrix valued function and $W:R\times R^n$. A new result for the existence of homoclinic orbits is established under a class of new superquadratic conditions. A homoclinic orbit is obtained as a limit of solutions of a certain sequence of boundary-value problems which are obtained by the minimax methods.

34C37Homoclinic and heteroclinic solutions of ODE
37J45Periodic, homoclinic and heteroclinic orbits; variational methods, degree-theoretic methods
58E05Abstract critical point theory
Full Text: DOI
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