Existence of periodic solutions of Hamiltonian systems with potential indefinite in sign

Infinitely Many Solutions for a Floquet-Type BVP with Superlinearity Indefinite in Sign

“…n; as a consequence of this and of goal 1 any solution x 0, p; и , with w x p g ⌫ l L , has at most i q i zeros in 0, . If we define 1 1 2…”

Non-autonomous second order Hamiltonian systems

“…Antonacci [7,8] gave conditions for existence of solutions with stronger constraints on the potential but without the homogeneity condition, and without the negative definite condition on the matrix. [131].…”

Ground state solutions for non-autonomous dynamical systems

“…Ding and Girardi [11] considered the case of (1) when the potential oscillates in magnitude and sign, (21) −ẍ(t) = B(t)x(t) + b(t)∇W (x(t)) , and found conditions for solutions when the matrix B(t) is symmetric and negative definite and the function W (x) grows superquadratically and satisfies a homogeneity condition. Antonacci [3,4] gave conditions for existence of solutions with stronger constraints on the potential but without the homogeneity condition, and without the negative definite condition on the matrix. Generalizations of the above results are given by Antonacci and Magrone [2], Barletta and Livrea [6], Guo and Xu [16], Li and Zou [24], Faraci and Livrea [15], Bonanno and Livrea [7,8], Jiang [21,22], Shilgba [39,40], Faraci and Iannizzotto [14] and Tang and Xiao [53].…”