[PDF] Top 20 A note on existence of infinitely many periodic solutions for second order nonlinear difference systems

... Hamiltonian systems and obtain the solvability condition of a periodic solution for discrete systems, based on operator ...study second-order discrete Hamiltonian systems, with ... See full document

... In this note, existence and uniqueness criteria for periodic solutions of 1.3 will be established. For this purpose, we will make use of a continuation theorem of Mawhin. Let X and Y be two ... See full document

... isfied. Then by Theorem ., we conclude that problem () has at least one solution which minimizes the functional ϕ in H T  . We note that F does not satisfy those of the results given in [–] (e.g., F does not ... See full document

... have become the assumptions in the searching for positive solutions of singular second-order equations and systems; see for instance Chu and Torres 2, Chu et al. 3, Franco and Torres 4, Jiang ... See full document

... of periodic solutions to difference sys- tems. When the systems are globally superquadratic or subquadratic, by restricting our discussion to the Nehari manifold, firstly, we study the existence ... See full document

... The existence of periodic solutions for problem ...with many solvability conditions by using the least action principle and the minimax methods, such as the coercive type potential condition ... See full document

... the existence of positive so- ...of periodic solu- tions for equation ...nontrivial periodic solutions of equation (1) under the following ... See full document

... the existence of periodic solutions and ho- moclinic solutions for second-order Hamiltonian systems have been intensively studied in many recent papers via ... See full document

... the existence and multiplicity ...by many scholars via critical point ...establish existence results of nontrivial standing wave solutions for discrete nonlinear Schrödinger ...of ... See full document

... We note that we could consider impulsive BVPs with an arbitrary finite number of impulses. However, for clarity and brevity, we restrict our attention to BVPs with one im- pulse. In addition, the di ff erence ... See full document

... the existence of periodic solutions of nonlinear, second-order difference equations of the form y(t + 2) + by(t + 1) + cy(t) = f (y(t)), where c = 0 and f : R → R is ... 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

... when p(t) ≡ p (a constant). The p(t)-Laplacian possesses more complicated nonlinearity than p-Laplacian; for example, it is inhomogeneous. The study of various mathematical problems with variable exponent growth ... See full document

... are periodic, that is (V0) and (F0) are satisfied, Zhao and Zhao [41] proved that ...infinitely many geometrically distinct solutions by using the Nehari manifold approach, where f and ∂f /∂u are ... See full document

... for nonlinear q-difference equations is still in the initial stages and many aspects of this theory need to be ...of nonlinear q-difference equations, a few works were done; see [–] and the ... See full document

... Using the least action principle, the existence of periodic solutions for some nonautonomous second order Hamiltonian systems is obtained.. Using minimax methods, the multiplicity of per[r] ... See full document

... On the other hand, the p(t)-Laplacian system has been studied by many authors in the last two decades, see, for example, [–] and the references cited therein. In [], by us- ing linking methods, the authors ... 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

... where f ∈ C([, ], R) and g ∈ C(R) are real functions. This kind of problem arises in the study of deflections of elastic beams on nonlinear elastic foundations. The problem has the following physical description: ... See full document

... In the paper we provide sufficient conditions for the existence of positive solutions for some second-order differential equation subject to periodic boundary conditions. Our method ... See full document