Twin monotone positive solutions to a singular nonlinear third-order differential equation

Twin monotone positive solutions to a singular nonlinear third-order differential equation

This paper discusses the existence of at least one or two nondecreasing positive solutions for the following singular nonlinear third-order differential equation x′′′(t)+ λα(t)f (t, x(t)) = 0, a < t < b, x(a)= x′′(a)= x′(b)= 0, where λ > 0 is a parameter, α ∈ C((a, b),R+), f ∈ C([a, b] × (0,+∞),R+), α(t) may be singular at t = a, b and f (t, s) may be singular at s = 0. Green’s function and the...

Twin Positive Periodic Solutions of Second Order Singular Differential Systems

In this paper, we study positive periodic solutions to singular second order differential systems. It is proved that such a problem has at least two positive periodic solutions. The proof relies on a nonlinear alternative of Leray–Schauder type and on Krasnosel’skĭı fixed point theorem on compression and expansion of cones.

Existence of positive solutions of a third order nonlinear differential equation with positive and negative terms

Boundedness of Solutions of a Third-order Nonlinear Differential Equation

Sufficient conditions are established for the boundedness of all solutions of (1.1), and we also present some sufficient conditions, which ensure that the limits of first and second order derivatives of the solutions of (1.1) tend to zero as t→∞. Our results improve and include those results obtained by previous authors ([3], [5]).

Existence and nonexstence of positive solutions for a singular higher-order nonlinear fractional differential equation

Abstract: In this paper, we establish some sufficient conditions for the existence and nonexstence of positive solutions to a general class of higher-order nonlinear fractional differential equation. The results are established by converting the problem into an equivalent integral equation and applying Banach fixed point theorem, nonlinear differentiation of Leray-Schauder type and the fixed po...