Second Boundary Value Problems for 2n-th Order Nonlinear Differential Equations

Sufficient conditions for the existence and uniqueness of second boundary value problems of two kinds of even order nonlinear differential equations are obtained. The proofs are based on the lemma on bilinear form, developed by A.C.Lazer, Schauder fixed point theorem and the Leray-Schauder degree theory, respectively.

Explicit Traveling Wave Solutions to Nonlinear Evolution Equations

First of all,some technical tools are developed.Then the author studies explicit traveling wave solutions to nonlinear dispersive wave equations,nonlinear dissipative dispersive wave equations,nonlinear convection equations,nonlinear reaction diffusion equations and nonlinear hyperbolic equations,respectively.

ON SPURIOUS ASYMPTOTIC NUMERICAL SOLUTIONS OF GAUSS SCHEME

In this paper, we discuss characteristics of Gauss scheme for numerical ordinary differential equations, which is a one-step high-order accurate difference scheme. We apply such scheme to some equations, and analyze the fixed point and stability accordingly.