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In this paper we extend the method of obtaining symmetries of ordinary differential equations to first order non-homogeneous neutral differential equations with variable coefficients. The existing method for delay differential equations uses a Lie-Bäcklund operator and an Invariant Manifold Theorem to define the operators which are used to obtain the infinitesimal generators of the Lie group. In this paper, we adopt a different approach and use Taylor’s theorem to obtain a Lie type invariance condition and the determining equations for a neutral differential equation. We then split this equation in a manner similar to that of ordinary differential equations to obtain an over-determined system of partial differential equations. These equations are then solved to obtain corresponding infinitesimals, and hence desired equivalent symmetries. We then obtain the symmetry algebra admitted by this neutral differential equation.
In this work, we establish some assumptions that guaranteeing the global exponential stability (GES) of the zero solution of a neutral differential equation (NDE). We aim to extend and improves some results found in the literature.
Content available remote Oscillation of higher-order half-linear neutral differential equations
In this paper, we establish some new oscillation criteria for the higher-order half-linear neutral differential equation (…). An example is given to illustrate the main results.
Content available remote Bounded oscillation for a class of even order neutral difference equations
We investigate bounded oscillation for the even order neutral delay difference equation delta'' (x(n) -cx(n-m) = pn(x-k), where u is even. The sufficient conditions obtained in this paper improve and generalize the results in related literature.
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