Oscillatory Solutions of Neutral Equations with Polynomial Nonlinearities

Oscillatory Solutions of Neutral Equations with Polynomial Nonlinearities

In 1, 2 , we have considered a lossless transmission line terminated by a nonlinear resistive load and parallel connected capacitance cf. Figure 1 . The nonlinear boundary condition is caused by the polynomial type V-I characteristics of the nonlinear load at the second end of the transmission line cf. Figure 1 . The voltage and current u x, t , i x, t of the lossless transmission line can be f...

Existence of Nonoscillatory and Oscillatory Solutions of Neutral Differential Equations with Positive and Negative Coefficients

In this paper, we study the existence of oscillatory and nonoscillatory solutions of neutral differential equations of the form ( x(t)− cx(t− r))′ ± (P (t)x(t− θ)−Q(t)x(t− δ)) = 0 where c > 0, r > 0, θ > δ 0 are constants, and P , Q ∈ C( +, +). We obtain some sufficient and some necessary conditions for the existence of bounded and unbounded positive solutions, as well as some sufficient condit...

Oscillatory and Asymptotic Behavior of Solutions of Second Order Neutral Delay Differential Equations with “maxima”

The authors establish some new criteria for the oscillation and asymptotic behavior of all solutions of the equation. (a(t)(x(t) + p(t)x(τ(t)))) + q(t) max [σ(t),t] x(s) = 0, t ≥ t0 ≥ 0, where a(t) > 0, q(t) ≥ 0, τ(t) ≤ t, σ(t) ≤ t, α is the ratio of odd positive integers, and ∫∞ 0 dt a(t) < ∞. Examples are included to illustrate the results. AMS Subject Classification: 34K11, 34K99

EXISTENCE OF PERIODIC SOLUTIONS IN TOTALLY NONLINEAR NEUTRAL DIFFERANCE EQUATIONS WITH VARIABLE DELAY

Existence and uniqueness of solutions for neutral periodic integro-differential equations with infinite delay

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