[PDF] Top 20 Existence of periodic solutions of a generalized Lienard equation

... the Lienard equation, the classical theorems on the existence of periodic orbits is well known ...which equation (1.1) has a periodic solution when the system has only one ... See full document

... In recent years, the existence of positive periodic solutions of the prey-predator model has been widely studied [–]. The qualitative analysis of predator-prey systems is an interest- ing ... See full document

... The organization of this paper is as follows. In section 2, we introduce some notations and lemmas, and state some preliminary results needed in later section, then we give the Green’s function of (1.1), which plays an ... See full document

... T-periodic solutions for ...the existence of positive periodic solutions for equation ...the periodic problem of ...-periodic solutions to ... See full document

... the existence of a periodic solution for p-Laplacian neutral Rayleigh ...some existence results of periodic solutions to p-Laplacian neutral Rayleigh ... See full document

... of periodic solutions for second order differential equations with ...the periodic problem for second order singular differential equations seems to be the work of Nagumo [] in ...the ... See full document

... where f ∈ C( R× (, ∞ ) × R× R ) is ω-periodic in t, and f (t, u, v, w) may be singular at u = . By applying of a fixed point theorem in cones, the author obtained that existence results of positive ... See full document

... the existence and uniqueness of positive periodic solutions for a class of first-order functional differential ...the existence of unique positive periodic solutions, but also be ... See full document

... as periodic oscillatory behavior, almost-periodic oscillatory properties, chaos, and bifurcation [11], and to the best of our knowledge, few authors considered the existence of periodic solu- ... See full document

... the existence of nontrivial periodic solutions to problem ...for solutions, which is a crucial step in applying the topological degree ... See full document

... In what follows, we consider the third-order differential equation (1.2) and obtain some conditions for the existence of periodic solutions for it. These con- ditions are applicable to many ... See full document

... the existence of the periodic solutions of the KDV type of equation with respect to time variable with periodic external ...original equation to the integral equation. The ... See full document

... To prove our results we adapt Mawhin’s continuation theorem in [2], and we give appropriate region for the system’s multiplicity by finding an a’priori bound.. To prove our assertion, we[r] ... See full document

... The periodic solution theory of differential equation and difference equation has impor- tant academic value and application ...the periodic solutions of neutral difference equations are ... See full document

... where f : [,T ] × [, ∞ ) × R → R and h : [, T ] → (, ∞ ) are continuous functions. Our study is motivated by current activity of many researchers in the area of theory and appli- cations of PVBPs; see, for example, ... See full document

... In this paper, in section 2, we state the sufficient condition for the asymptotic stability of Equation (1). Next, in section 3, we study the existence of periodic solutions of Equation ... See full document

... continuous periodic one-parameter group of linear operators in a Banach ...the existence of periodic solutions of a linear differential equation of the nth order with constant coefficients ... See full document

... the generalized neutral operator A which will be helpful for further studies of differential equations with this neutral operator; in Section , by Mawhin’s continuation theorem, we obtain the existence of ... See full document

... the existence of periodic solutions of functional differential equations which was done by using the Mawhin’s coincidence degree theory we refer to [5, 7, 8, ... See full document

... In the section, we first use the saddle point theorem (see Theorem 4.6, [12] or [10]) to prove that problem (1.1) has at least one solution. Then, to prove that problem (1.1) has multiple periodic solutions, ... See full document