[PDF] Top 20 Periodic solutions for a class of nonautomous second order systems

... x∈ .Hence we have, by (8),(b) is satisfied. It follows from the generalized saddle point theorem (Theorem 1.7 in [4]) that has at least r + 1 critical points .Hence ϕ has at least r + 1 geometrically distinct critical ... 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

... of periodic solutions of functional di ff erential equations, one commonly uses methods of fixed point theory, coincidence degree theory, Fourier anal- ysis, and so ...multiple periodic ... See full document

... Compared to system (.), the neutral functional differential system (.) admits four control parameters p, q, λ, s. We aim to derive conditions in terms of these four control parameters for the existence and ... 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 ... See full document

... In this paper, the main purpose is to study the multiplicity of periodic solutions for sys- tems (.) via some recent critical point theorems for strongly indefinite functionals. In order to achieve ... See full document

... Introduction and Statement of the Main Results In this paper we shall study the existence of periodic solutions of the second-order differential equation of the form.. We note that the s[r] ... See full document

... one periodic solution. The periodic solutions which we get appear either as saddle points or as minimizers of the energy functional associated to problem ...distinct periodic solutions ... 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 ... 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

... 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 ... See full document

... The paper is organized as follows. In Section , we establish the variational structure of () and transfer the existence of the solution into the existence of a critical point of the corresponding functional. The dual ... See full document

... of periodic solutions and ho- moclinic solutions for second-order Hamiltonian systems have been intensively studied in many recent papers via variational methods; see [–] and ... 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 solutions in these ...of periodic and homoclinic solutions for a class of second-order differential equations of the form () in the case μ = , via variational methods, the ... See full document

... where ϕx ox as |x| → ∞ and et is a 2π-periodic function. After introducing new variables, the differential equation 1.3 can be changed into a Hamiltonian system. Under some suitable assumptions on ϕx and et, by ... See full document

... one periodic solution, while here by Theorem ...many periodic solutions and quasi-periodic solutions of ...rotating periodic solution is just a ... 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

... Remark . When F(t, x) = –a cosx – e(t)x (a ≥ ), system (.) is a discrete form of forced equations studied by Mawhin and Willem [–], in which they require the assumption that the forced potential is ... See full document

... The existence of periodic solutions for problem (1.1) has been studied extensively, a lot of existence and multiplicity results have been obtained, we refer the readers to [1-13] and the reference therein. ... See full document