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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)
In this paper sufficient conditions are obtained for oscillation of all solutions of a class of nonlinear neutral delay difference equations of the form ∆ 2 (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 sublin-ear or superlinear. 1 Introduction Recently, a good deal of work has been(More)
In this paper, we study the existence and multiplicity of periodic solutions of the following second-order Hamiltonian systems ¨ x(t) + V ′ (t, x(t)) = 0, where t ∈ R, x ∈ R N and V ∈ C 1 (R × R N , R). By using a symmetric mountain pass theorem, we obtain a new criterion to guarantee that second-order Hamiltonian systems has infinitely many periodic(More)