Abstract
Abstract We consider a system of ODEs of mixed order with derivative terms appearing in the non-linear function and show the existence of a solution which does not oscillate for such system. We applied the fixed point technique to show that under certain conditions there exists at least one solution to the system which is not only non-oscillating, but also asymptotically constant.
Highlights
Systems of di erential equations arise while modelling many situations
In [1], the authors discuss some qualitative properties of elliptic systems of the type
They considered the existence of positive radial solutions for this system
Summary
Systems of di erential equations arise while modelling many situations. We will look at few systems of coupled ODEs which arise in nature. The χ −SHG equations arise while studying the Parametric interactions of intense light signals in materials with second-order non-linearities. We consider the following generalized version of coupled system of non-linear ordinary di erential equations. Lot of work is done in providing conditions to nd non oscillating solutions of systems and equations. ]. In most of these article authors proved conditions for non oscillation or positive solutions for either lower order systems which are fully coupled or higher order systems which are weakly coupled. Graef et al [13] considered the following second order system which is fully coupled. In this article we presented di erent conditions under which the existence of a non-oscillating solution for system (1.5) is guaranteed. At the end we apply the theory developed on a theoretical example
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