Quasiperiodic Solutions for Nonlinear Differential Equations of Second Order with Symmetry

In this paper,we study the existence of quasi-periodic solutions and the bound- edness of solutions for a wide class nonlinear differential equations of second order.Using the KAM theorem of reversible systems and the theory of transformations,we obtain the existence of quasi-periodic solutions and the boundedness of solutions under some reasonable conditions.

Existence of Three Positive Solutions for Some Second-Order M-Point Boundary Value Problems

By using fixed-point theorems, some new results for multiplicity of positive solutions for some second order m-point boundary value problems are obtained.The associated Green＇s function of these problems are also given.

TYPES AND CRITERIA OF NONOSCILLATORY SOLUTIONS FOR A CLASS OF SECOND ORDER NEUTRAL FUNCTIONAL DIFFERENTIAL EQUATIONS WITH NONPOSITIVE COEFFICIENTS

In this paper we discuss the types and criteria of nonoscillatory solutions for the fol-lowing second order neutral functional differential equation with nonpositive coefficients

Smoothness of the Gradient of Weak Solutions of Degenerate Linear Equations

Let Q（x） be a nonnegative definite, symmetric matrix such that √Q（X） is Lipschitz con- tinuous. Given a real-valued function b（x） and a weak solution u（x） of div（QVu） = b, we find sufficient conditions in order that √Qu has some first order smoothness. Specifically, if is a bounded open set in Rn, we study when the components of vVu belong to the first order Sobolev space W1＇2（Ω） defined by Sawyer and Wheeden. Alternately we study when each of n first order Lipschitz vector field derivatives Xiu has some first order smoothness if u is a weak solution in Ω of ^-^-1 X^Xiu ＋ b = O. We do not assume that {Xi}is a HSrmander collection of vector fields in ~. The results signal ones for more general equations.

The J Integral of a Slightly Curved Elasticity-plasticity Crack when Enduring Quasi Static Loads

The J Integral of an elastic-plastic curved crack under quasi-static loads has been mainly worked in the paper,and the J Integral has been calculated as a practical application of a second order perturbation method and theorem of surname KA where the effect of quasi-static applied stresses and normal and shear stresses on the boundaries of plasticity area are synthetically taken into consideration.A regular pattern of variations of the J Integral of an elastic-plastic curved crack with the variations of curved crack shape parameters under different quasi-static loads has been mainly carried out.Continuity and unity of a elastic-plastic fracture and linear elastic fracture has been demonstrated from the viewpoint of the mechanical parameter of the curved crack tip J integral.The elastic-plastic slightly curved crack tip J integral has been calculated approximately,an integral loop having been reasonably selected and continuity and unity of the fracture characteristic of centre penetration straight line crack and curved crack have been demonstrated.

Effeet of Hardening on Elastic-plastic Curved Crack Tip Displacement Under Dynamic Load

In this article, elastic-plastic curved crack tip opening displacement maximum in hardened material under dynamic loads has been studied, and curved crack tip opening displacement has been calculated as a practical application of a second order perturbation method and theorem of surname KA, where the effects of dynamic applied stresses and dynamic normal and shear stresses on the boundaries of plastic area are synthetically taken into considerations. Diagrams have been constructed to analyz the transformation relationships between the curved crack tip opening displacement and the work hardening exponents. Curved crack tip opening displacement will decrease with the increasing of hardening exponents in hardened material. The decrease extent of curved crack tip dynamic opening displacement will be more and more severe when hardening exponents increase evenly. Maximum dynamic opening displacement of curved crack tip will decrease when external load decrease with the same hardening exponents