[PDF] Top 20 Periodic solutions for some phi-Laplacian and reflection equations

... positive solutions is treated in [], the existence of an exact number of solutions in [] and topological existence results can be found in ...the solutions are studied in [, ...p- ... See full document

... We obtain a sufficient condition for the existence of periodic and subharmonic solutions of second-order p-Laplacian di ff erence equations using the critical point theory. Copyright © 2007 P. ... See full document

... of periodic solutions for some types of p-Laplacian neutral differential equations has attracted much attention from researchers; see [–] and the references cited ...the ... See full document

... are some papers concerning related equations or ab- stract spaces with variable ...differential equations (PDEs) with a variable ...to some standard differential operator with variable ...of ... See full document

... In addition, problem (1.2) is also very interesting from a purely mathematical point of view. When the variable exponent p(k) ≡ 2, discrete p(k)-Laplacian system (1.2) becomes the second order discrete Hamiltonian ... See full document

... from some problems associated with differential geometry and physics such as com- bustible gas dynamics, have been studied widely (see [–] and the references ...of periodic solutions for the ... See full document

... extend some recent results due to Liu ...of periodic solutions for a kind of Lienard type p-Laplacian equation, Nonlinear Analysis TMA, 69, 724–729, 2008 ... See full document

... In recent years, the existence of periodic solutions for second-order Li´enard equations u + f (u,u )u + g (u) = e(t,u,u ) (1.1) and its special case have been studied by many researchers, we refer ... See full document

... and two results Theorems 3.1 and 3.2 on the existence of periodic solutions were obtained. Ge and Ren 5 promoted Mawhin’s continuation theorem to the case which involved the quasilinear operator ... See full document

... Remark 3.1. Suppose that F(t, ·) is continuously differentiable in x and p(t) ≡ p, then condition (B1) reduces to the well-known Ambrosetti-Rabinowitz condition (see [19]), which was introduced in the context of ... See full document

... of periodic solutions, such as the Lyapunov second method, fixed point theorem, coincidence degree theory, the Yoshizawa type theorem, and the Massera type theorem, see [, –] and references ... See full document

... The paper is organized as follows. Section 2 is devoted to the proof of the existence of periodic solutions for problem (1.1) by using the Leray-Shauder fixed point theorem, which is di ff erent from that ... See full document

... decades, periodic problems involving the scalar p-Laplacian were studied by many authors, especially for the second-order and three-order p-Laplacian differential equation, see 1–8 and the references ... See full document

... decaying solutions of (), which are posi- tive decreasing on the whole interval [, ...decaying solutions are difficult to establish, due to the problem to find sharp upper and lower bounds; see, ... See full document

... of periodic solution is studied for p-Laplacian Liénard equations with singular at x = 0 and x = ...theory, some new results are obtained, and an example is given to illustrate the ... See full document

... periodic solutions. Also, there are many works about reaction diffusion equations without nonlocal term; one can see [–] and the references therein, and the boundary value condition and research ... See full document

... obtain some results like The- orem A and Theorem B for system ...obtain some existence and multiplicity results of homoclinic so- lutions for system ...not periodic in n and possesses (p, ... See full document

... After that, by using the above results, many researchers studied the existence of periodic solutions for some kinds of differential equations; see [–]. In a recent paper [], when the ... See full document

... Existence and multiplicity of solutions of the periodic problems driven by the p- Laplacian have been obtained in the literature by many people (see [–]). Many solv- ability conditions for problem ... 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