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Existence of periodic solutions to second-order Hamiltonian systems with potential indefinite in sign. (English) Zbl 1157.37329

From the text: The authors study second-order systems of differential equations of the form x ¨+W ' (t,x)=0, where W(t,x)=(A(t)x,x)+b(t)V(x) with A(·) a continuous, T-periodic matrix-valued function, (·,·) denotes the scalar product in n , b(·) is a continuous, T-periodic real function and V(·)C 2 ( n ,) is a nonnegative, superquadratic function.

Using variational methods and applying a linking theorem, the authors prove the existence of a nontrivial T-periodic solution in a case when A(t) is not negative definite and several additional technical conditions are satisfied.

37J45Periodic, homoclinic and heteroclinic orbits; variational methods, degree-theoretic methods
34C25Periodic solutions of ODE
47J30Variational methods (nonlinear operator equations)
58E05Abstract critical point theory