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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)

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.

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