[PDF] Top 20 Stability Analysis of Periodic Solutions of Some Duffing’s Equations

... global stability of periodic solution was achieved through the construction of a suitable and complete Lyapunov function for the hard spring system using Cartwright ...the stability behaviours of the ... See full document

... almost periodic functions were first introduced in [10, 11] by ...(integral) equations, many authors [5, 9, 12, 13, 14, 25] apply the asymptotic property of the functions to deter- mine the existence of ... See full document

... the solutions. With special attention to the boundedness of the solutions and the instability of the unique equilibrium point of linearized system, some sufficient conditions to guarantee the ... See full document

... difference equations is the stability of the solutions of the treated ...linear equations or Lyapunov functions, have been developed for both type of equations, see [7] for ordinary ... See full document

... a periodic time scale such that 0 ∈ T ...the analysis of qualitative theory of periodic and positive periodic solutions of neutral dynamic ... See full document

... evolution equations with delay in Banach ...establish some new existence theorems of periodic mild solutions for the ...the equations have an asymptotically stable ω -periodic ... See full document

... type periodic solution is very difficult to prove, see, for example, Bernstein and Katok’s work ...differential equations, such as Hamiltonian systems [–], reversible systems [, ] and nonlinear ... See full document

... differential equations has become an active area of in- vestigation due to their applications in fields such as mechanics, electrical engineering, medicine biology (see ...and stability of almost ... See full document

... The relation between (i) and (ii) is the mathematical tools used by physicists in connection with Schrödinger equations with periodic potentials [4]. We will use the same tools used before like the direct ... See full document

... of periodic solutions of the Duffing-type equation ...lower solutions and coincidence degree theory and a series of existence results of nontrivial solutions for the Duffing-type equations ... See full document

... t, s, j ) of (1.3) is said to be stable, if for any s Î R, ε > 0, there is a number δ = δ(s, ε) > 0, such that for any other solution y(t, s, ψ) of ...||x(t, s, )-y(t, s, ... See full document

... of periodic solutions by various methods, such as a generalized form of the Poincaré-Birkhoff theorem, critical point theory, phase-plane analysis com- bined with shooting methods or fixed point ... See full document

... the periodic boundary value problems PBVPs for short for second-order ordinary or functional differential equations with or without impulse effects; see 1–24 and the references ... See full document

... differential equations describe many problems in the applied sciences, such as the Brillouin focusing system and nonlinear ...of periodic solutions for singular dif- ferential equations have ... See full document

... and Stability for Some Partial Nentral Functional Differential Equations with Infinite ...Mathematical Analysis and Applications , 294, ... See full document

... almost periodic and on ergodic ...uniqueness solutions of some difference equations using polynomial ...to some second order differential equation with a piecewise constant ... See full document

... The influence of the quintic-septic nonlinearity and linear damping coefficients on the bifurcation sequences are investigated and reported in Figures 12. From these figures it is found that decreasing of the dissipation ... See full document

... The organization of this paper is as follows. In Section 2, we introduce some nota- tions and definitions, and state some preliminary results needed in later sections. We then study, in Section 3, the ... See full document

... in equations (.)-(.) satisfies  T f (x(t))x (t) dt = , which is crucial for obtaining an a priori bounds of all the possible T -periodic solutions for equation (.)-equation (.). However, the ... See full document

... The topic of singular boundary value problems has been of substantial and rapidly grow- ing interest for many scientists and engineers. The importance of such investigation is emphasized by the fact that numerical ... See full document