[PDF] Top 20 Periodic solutions to the Liénard type equations with phase attractive singularities

... is investigated in the presented paper. Here, f , g : (, + ∞ ) → R are continuous, hav- ing possible singularities at zero, and h : [, ω] × R → R is a Carathéodory function, i.e., h(·, x) : [, ω] → R is ... See full document

... generalized Liénard equations with singularities of attractive and repulsive type, where the nonlinear term g has a singularity at the ...that singularities of attractive ... See full document

... on periodic solutions for Liénard equations (see [–] and the references cited ...study Liénard equation in the literature, including Mawhin’s coincidence degree theorem [, , ], ... See full document

... the equations with a singular- ity began with some work of Forbat and Huaux ...the equations studied previously were either of the type of Duffing equations [–, –] or of the type ... See full document

... lower solutions, was first used by Lazer and Solimini in the pioneering paper [] for considering the problem of a periodic solution to a second order differential equations with ...p-Laplacian ... See full document

... conservative equations with weak singularities, the corresponding ones of the Liénard equation with a weak singularity of repulsive type is considerably ...singular Liénard equation of ... See full document

... on periodic solutions for Duffing equations with a singularity (see [1–5, 7–11] and the references cited therein), in account of its applications in applied ... See full document

... The structure of the paper is as follows. Section  contains the tools needed in the proofs. In Section , we state and prove the main results and develop some corollaries for the equation with a singularity of mixed ... See full document

... positive periodic solutions for equation ...positive solutions to the periodic problem associated to the equation of Rayleigh–Plesset ... See full document

... of periodic solutions for neutral differential equations with sin- gularity has been researched (see [7–9, ...positive periodic solution of fourth-order neutral Liénard equation with a ... See full document

... doubly periodic solutions for a single regular tele- graph equation or regular telegraph system, see, for example, the papers [–] and the references ... 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 here [■] denotes the ... See full document

... approach previously applied to the study of binary alloys on the example of Kahn- Hilliard equation with delay argument to applications to binary mixtures [13]-[16] and to binary polymer blends [17]-[19]. Such problem ... See full document

... and the existence of a bounded solution and whenever the phase space satisfies the axioms A–C, but here it is also necessary that B verifies the fading memory property. If the particular solution is asymptotically ... See full document

... of periodic solutions for the prescribed mean curvature equation has attracted many researchers’ attention ...the periodic solutions for nonlinear equations with mean curvature-like ... See full document

... are periodic functions of period ω and τ >0 is a fixed real ...has periodic solutions if and only if (1) holds for all periodic solutions y(t) of period ω of the adjoint ... See full document

... • iii CONTENTS STATEMENT i ACKNOWLEDGEMENTS ii CHAPTER I: Introduction l CHAPTER II: The frequency basis of almost periodic solutions of almost periodic differential equations 8 CHAPTER [r] ... See full document

... of periodic solu- tions for neutral differential ...of periodic solu- ...of periodic solutions by using the generalization of Mawhin’s continuation ... 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 existence of ... See full document

... (for equations without the integral term) that f (0) = 0 is almost necessary to obtain the convergence in derivative at t = ...For equations with the integral term, we also need this condition in [2] and ... See full document