We use Krasnoselskii’s fixed point theorem to show that the nonlinear neutral differential equation with delay d dt [x(t)− ax(t− τ)] = r(t)x(t)− f(t, x(t− τ)) has a positive periodic solution. An example will be provided as an application to our theorems. AMS Subject Classifications: 34K20, 45J05, 45D05

In this work, we investigate the oscillation criteria for second order neutral delay differential equations of the form (r(t)[y(t)+ p(t)y(δ (t))]′)′ +q(t)G(y(τ(t))) = 0 and (r(t)[[y(t)+ p(t)y(δ (t))]′]α )′ +q(t)(yβ (τ(t))) = 0, where α and β are the ratio of odd positive integers. Mathematics subject classification (2010): 34C10, 34C15.

Nonoscillatory solutions of a general class of second order functional neutral differential equations of the form

This paper is concerned with the oscillation of second-order nonlinear neutral differential equations of the form [ r(t)[(x(t) + p(t)x(σ(t)))′]γ ]′ + f(t, x(τ(t))) = 0, by using a generalized Riccati’s technique and integral averaging technique, we establish new oscillation results which handle some cases not covered by known criteria.

Neutral stochastic functional differential equations NSFDEs have recently been studied intensively. The well-known conditions imposed for the existence and uniqueness and exponential stability of the global solution are the local Lipschitz condition and the linear growth condition. Therefore, the existing results cannot be applied to many important nonlinear NSFDEs. The main aim of this paper i...

Oscillation criteria, extended Kamenev and Philos-type oscillation theorems for the nonlinear second order neutral delay differential equation with and without the forced term are given. These results extend and improve the well known results of Grammatikopoulos et. al., Graef et. al., Tanaka for the nonlinear neutral case and the recent results of Dzurina and Mihalikova for the neutral linear ...

in this paper an approximate analytical solution of the fractional zakharov-kuznetsov equations will be obtained with the help of the reduced differential transform method (rdtm). it is in-dicated that the solutions obtained by the rdtm are reliable and present an effective method for strongly nonlinear fractional partial differential equations.

in recent years, numerous approaches have been utilized for finding the exact solutions to nonlinear partial differential equations. one such method is known as the new extended (g'/g)-expansion method and was proposed by roshid et al. in this paper, we apply this method and achieve exact solutions to nonlinear partial differential equations (nlpdes), namely the benjamin-ono equation. it i...

In this paper, some sufficient conditions are established for the oscillation of second-order neutral functional differential equation [ r(t)[x(t)+ p(t)x(τ(t))]′ ]′+q(t) f (x(σ(t))) = 0, t ≥ t0, where ∫ ∞ t0 dt/r(t) = ∞, or ∫ ∞ t0 dt/r(t) < ∞, 0 ≤ p(t) ≤ p0 < ∞. The results obtained here complement and improve some known results in the literature. 2010 Mathematics Subject Classification: 39A21,...

In this paper we are concerned with a neutral differential equation with a deviated argument in an arbitrary Banach space X. To study the existence and uniqueness of a solution of the problem considered, we use the theory of the analytic semigroups and the fixed point arguments. Finally, we give an example to demonstrate an application of the abstract results.