[PDF] Top 20 Lagrangian Stability of a Class of Second-Order Periodic Systems

... The proof of Theorem 1.1 is based on Moser’s small twist theorem for reversible mapping. It mainly consists of two steps. The first one is to find an equivalent system, which has a nearly integrable form of a reversible ... See full document

... the periodic and subharmonic solutions are investigated for a class of second-order non-autonomous ordinary differential equations with a ... See full document

... of periodic solutions to ordinary differential systems as well as partial differential equa- tions (see ...of periodic solutions for delay differential ...of periodic solutions for the func- ... See full document

... In this work, we have established an existence result for nonconstant periodic solutions of a class of second-order systems with p(t)-Laplacian. For p(x) is a constant p, it is easy to ... See full document

... the second-order differential equation u = f (t, u, u ), we generally consider impulses in the position u and u ...the second-order impulsive Hamilto- nian system ...of periodic and ... See full document

... Tang, CL, Wu, XP: Periodic solutions for a class of nonautonomous subquadratic second order Hamiltonian systems.. Chang, KC: Variational methods for non-differentiable functionals and the[r] ... See full document

... With periodic potentials, that is, (2) holding with r=N, the existence and multiplicity theorems are obtained for the nonautonomous second-order system (1) in [1] and [2] ...nonautonomous ... See full document

... Now, the functional satisfies all hypotheses of the saddle point theorem (see [], Theorem .), so has at least a critical point. Therefore, problem (.) possesses at least one T -periodic solution in W T ,p(t) ... See full document

... In this paper, by using the mountain pass theorem, we investigate the existence of subharmonic weak solutions for a class of second-order impulsive Lagrangian systems with damped term ... See full document

... of periodic solutions for problem ...the periodic type potential conditions (see []), the even type potential condition (see []), the subquadratic potential condition in Rabinowitz’s sense (see []), the ... See full document

... Variational methods are very powerful techniques in nonlinear analysis and are exten- sively used in many disciplines of pure and applied mathematics, including ordinary and partial differential equations, mathematical ... See full document

... Jiang, Q, Tang, C: Periodic and subharmonic solutions of a class of subquadratic second-order Hamiltonian systems. Wang, Z, Zhang, J: Periodic solutions of a class of second order non-au[r] ... See full document

... of periodic solutions of difference equations by using critical point theory (see [–]), the ex- istence and multiplicity of periodic solutions for system ...classical second-order Hamiltonian ... See full document

... Using the least action principle, the existence of periodic solutions for some nonautonomous second order Hamiltonian systems is obtained.. Using minimax methods, the multiplicity of per[r] ... See full document

... the second order system x = g(t,x) admits rotating periodic solutions with form u(t + T) = Qu(t) for any orthogonal matrix Q when the nonlinearity g admits the Hartman-type ... See full document

... of periodic solutions for the sec- ond order nonautonomous Hamiltonian systems with p-Laplacian, here p > 1, it is assumed that the nonlinearity ∇F (t, x) may grow slightly slower than |x| p-1 , a ... See full document

... multiple periodic solutions of second order Josephson-type differential systems with partially periodic potential by using the minimax methods in critical point theory, which generalize ... See full document

... to know how many degree of FWL error will cause closed-loop instability. This means that we would like to know the largest open “hypercube” in the perturbation space within which the digital system remains stable. The ... See full document

... (see [] and the references therein). The interest in studying the equations with a singular- ity began with some work of Forbat and Huaux []. Later, the interest in such problem was renewed by Gordon in [, ], and ... See full document

... the Cartesian product of two cones in the space PC[0, 1], and using the well-known fixed point theorem of cone expansion and compression, we obtain conditions for the existence and multiplicity of positive solutions of ... See full document