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Sufficient conditions are established for the oscillation of the linear two-dimensional difference system ∆x n = p n y n , where { p n }, {q n } are nonnegative real sequences. Our results extend the results in the literature.

The oscillation criteria are investigated for all solutions of second order nonlinear neutral delay differential equations. Our results extend and improve some results well known in the literature see ([14] theorem 3.2.1 and theorem 3.2.2 pp.385-388). Some examples are given to illustrate our main results.

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)

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