Bounds for Asymptote Singularities of Certain Nonlinear Differential Equations

ON TE EXISTENCE OF PERIODIC SOLUTION FOR CERTAIN NONLINEAR THIRD ORDER DIFFERENTIAL EQUATIONS

Correlation between Pole Location and Asymptotic Behavior for Painlevé I Solutions

We extend the technique of asymptotic series matching to exponential asymptotics expansions (transseries) and show that the extension provides a method of finding singularities of solutions of nonlinear differential equations, using asymptotic information. This transasymptotic matching method is applied to Painlevé’s first equation. The solutions of P1 that are bounded in some direction towards...

ALGEBRAIC NONLINEARITY IN VOLTERRA-HAMMERSTEIN EQUATIONS

Here a posteriori error estimate for the numerical solution of nonlinear Voltena- Hammerstein equations is given. We present an error upper bound for nonlinear Voltena-Hammastein integral equations, in which the form of nonlinearity is algebraic and develop a posteriori error estimate for the recently proposed method of Brunner for these problems (the implicitly linear collocation method)...

Application of the linear Differential Equations on the Plane and Elements of Nonlinear Systems, In Economics

In recent years, it has become increasingly important to incorporate explicit dynamics in economic analysis. These two tools that mathematicians have developed, differential equations and optimal control theory, are probably the most basic for economists to analyze dynamic problems. In this paper I will consider the linear differential equations on the plane (phase diagram) and elements of nonl...

The existence results for a coupled system of nonlinear fractional differential equations with multi-point boundary conditions

In this paper, we study a coupled system of nonlinear fractional differential equations with multi-point boundary condi- tions. The differential operator is taken in the Riemann-Liouville sense. Applying the Schauder fixed-point theorem and the contrac- tion mapping principle, two existence results are obtained for the following system D^{alpha}_{0+}x(t)=fleft(t,y(t),D^{p}_{0+}y(t)right), t in (0,...