Jianchu Jiang

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In this paper, two interesting oscillation criteria are obtained for all solutions of the nonlinear delay difference equation of the form xnþ1 xn þ pnf ðxn l1 ; xn l2 ; . . . ; xn lmÞ 1⁄4 0; n 1⁄4 0; 1; 2; . . . The results extend some well-known results in the literature. And two examples are given to demonstrate the advantage of our results. 2002 Elsevier(More)
A non-trivial solution of (1) is called oscillatory if for every N > 0 there exists an n > N such that X,X n + , 6 0. If one non-trivial solution of (1) is oscillatory then, by virtue of Sturm’s separation theorem for difference equations (see, e.g., [S]), all non-trivial solutions are oscillatory, so, in studying the question of whether a solution {x,> of(More)
Sufficient conditions are established for the oscillation of the linear two-dimensional difference system ∆xn = pn yn, ∆yn−1 = −qnxn, n ∈ N (n0) = {n0, n0 + 1, . . .}, where {pn}, {qn} are nonnegative real sequences. Our results extend the results in the literature. c © 2007 Elsevier Ltd. All rights reserved.
In this paper sufficient conditions are obtained for oscillation of all solutions of a class of nonlinear neutral delay difference equations of the form ∆(y(n) + p(n)y(n−m)) + q(n)G(y(n − k)) = 0 under various ranges of p(n). The nonlinear function G,G ∈ C(R,R) is either sublinear or superlinear. Mathematics Subject classification (2000): 39 A 10, 39 A 12
In this paper, we study the existence and multiplicity of periodic solutions of the following second-order Hamiltonian systems ẍ(t) + V ′(t, x(t)) = 0, where t ∈ R, x ∈ R and V ∈ C(R × R ,R). By using a symmetric mountain pass theorem, we obtain a new criterion to guarantee that second-order Hamiltonian systems has infinitely many periodic solutions. We(More)