Positive solutions of a quadratic integro-differential equation

Positive Solutions of Volterra Integro–differential Equations

We present some sufficient conditions such that Eq. (1) only has solutions with zero points in (0,∞). Moreover, we also obtain some conditions such that Eq. (1) has a positive solution on [0,+∞). The motivation of this work comes from the work of Ladas, Philos and Sficas [5]. They discussed the oscillation behavior of Eq. (1) when P (t, s) = P (t− s) and g(t) = t. They obtained a necessary and ...

Existence of positive solutions for a boundary value problem of a nonlinear fractional differential equation

This paper presents conditions for the existence and multiplicity of positive solutions for a boundary value problem of a nonlinear fractional differential equation. We show that it has at least one or two positive solutions. The main tool is Krasnosel'skii fixed point theorem on cone and fixed point index theory.

Triple Positive Solutions for Boundary Value Problem of a Nonlinear Fractional Differential Equation

Triple positive solutions of nth order impulsive integro-differential equations

In this paper, we prove the existence of at least three positive solutions of boundary value problems for nth order nonlinear impulsive integrodifferential equations of mixed type on infinite interval with infinite number of impulsive times. Our results are obtained by applying a new fixed point theorem introduced by Avery and Peterson.

Positive Solutions of Neutral Delay Differential Equation

Neutral delay differential equations contain the derivative of the unknown function both with and without delays. Some new phenomena can appear, hence the theory of neutral delay differential equations is even more complicated than the theory of non-neutral delay equations. The oscillatory behavior of the solutions of neutral systems is of importance in both the theory and applications, such as...