Behavior of Solutions of a Nonlinear Ordinary Differential Equation

BEHAVIOR OF SOLUTIONS TO A FUZZY NONLINEAR DIFFERENCE EQUATION

In this paper, we study the existence, asymptotic behavior of the positive solutions of a fuzzy nonlinear difference equation$$ x_{n+1}=frac{Ax_n+x_{n-1}}{B+x_{n-1}}, n=0,1,cdots,$$ where $(x_n)$ is a sequence of positive fuzzy number, $A, B$ are positive fuzzy numbers and the initial conditions $x_{-1}, x_0$ are positive fuzzy numbers.

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.

New Result in the Ultimate Boundedness of Solutions of a Third-order Nonlinear Ordinary Differential Equation

Sufficient conditions are established for the ultimate boundedness of solutions of certain third-order nonlinear differential equations. Our result improves on Tunc’s [C. Tunc, Boundedness of solutions of a third-order nonlinear differential equation, J. Inequal. Pure and Appl. Math., 6(1) Art. 3,2005,1-6].

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

Existence of periodic solutions for a semilinear ordinary differential equation

Dancer [3] found a necessary and sufficient condition for the existence of periodic solutions to the equation ẍ+ g1(ẋ) + g0(x) = f(t) . His condition is based on a functional that depends on the solution to the above equation with g0 = 0. However, that solution is not always explicitly known which makes the condition unverifiable in practical situations. As an alternative, we find computable bo...