[PDF] Top 20 Multiple periodic solutions to a class of second order nonlinear mixed type functional differential equations

... x(t) + cx(t − τ) + g t,x(t − σ ) = p(t), (1.1) where τ, σ, and c are constants in R with τ ≥ 0, σ ≥ 0, | c | < 1, g (t,x) is a T (> 0)-periodic function in t > 0, and for an arbitrary bounded domain E ⊂ ... See full document

... of periodic solutions of delay differential equations; see, for example, ...of periodic solutions for delay differential equations include the dual Lyapunov method, the Fourier ... 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

... lower solutions method and monotone iterative method) (see, for example, [–] and references ...of solutions for impul- sive problems have been thoroughly investigated by [–] using variational ... See full document

... of functional differential equations have been studied in recent ...of functional differential equations received much less attention, which is due mainly to the technical ... See full document

... In [], Mawhin and Willem established a variational structure which enables us to reduce the existence of solutions for problem (.) to the existence of critical points of the fol- lowing energy ... See full document

... of solutions for second-order differential delay equation by using a variational ...Kaplan-Yorke type periodic solutions of second- order differential ... See full document

... all solutions of equation ...in order that every solution of equa- tion ...non-oscillatory solutions of equation ...the solutions of equation ... See full document

... upper solutions and the coincidence degree theory ...of solutions for impulsive differential equation boundary value prob- lems ...Neumann nonlinear differen- tial problem in [] (see also [, ] ... See full document

... in nonlinear analysis and are exten- sively used in many disciplines of pure and applied mathematics, including ordinary and partial differential equations, mathematical physics, and geometrical ...of ... See full document

... guarantee that every solution f ≡  of equation () has infinite order? There has been much work on this subject. For example, it follows from the work by Gunderson [], Hellerstein et al. [] that if A(z) and B(z) ... See full document

... antiperiodic solutions for nonlinear evolution equations is closely related to the study of periodic solutions, and it was initiated by Okochi ... See full document

... evolution equations of second-order in case f ·, x· h ∈ L 2 0, T; V ∗ are given by ...and second-order equations. The well-posedness of solutions for delay evolution ... See full document

... 1 − H(β + γ) . (3.11) As a result, we obtain the desired bound. We see that the bound on all possible solutions to (3.4) is independent of λ. Applying Scheafer fixed point theorem, A has at least one fixed point, ... See full document

... periodical solutions of th e second-order neutral delay differential equations w ith piecewise constant a rgum ents of th e form x"(t) + px "( t - 1) = qx(2[£+-]) + f (t), w ... See full document

... of periodic solutions have attracted many authors’ attention and ...of nonlinear functional analysis have been applied to research the periodic problems of Equation (), such as the ... See full document

... Examples In this section, we give some examples on our approach for reduction and finding solutions of nonlinear second order ordinary differential equations, these equations and more eq[r] ... See full document

... Inspired by the work of Li [5], we give sufficient conditions for the existence and uniqueness of the 2π -periodic solution of 1.1 by using the initial value problem method and homeomorphi[r] ... See full document

... denote the quasi-derivative of y(x), we call the periodic boundary conditions which are impor- tant representatives of nonseparated boundary conditions. The nonlinearity f ∈ C(( R /T Z ) × (0, ∞), R ). We are ... See full document

... 0, n ∈ Z, 1.5 has been studied. Other interesting contributions can be found in some recent papers 7–11 and in references contained therein. It is interesting to study second-order nonlinear ... See full document