ON THE STRUCTURE OF SOLUTIONS OF LINEAR PARTIAL DIFFERENTIAL EQUATION sum from (i j≤n) (a_(ij)p~iq~j(■))=0 WITH TWO INDEPENDENT VARIABLES AND CONSTANT COEFFICIENTS

This paper is a continuation of [1].In this paper,the solutions of the more generallinear partial differential equation (?) with two independent variables andconstant coefficients are discussed in detail.The general solution which can be used in theapproximation to the conditions of the definite solution of the practical problems ispresented.To illustrate the use of the results obtained in this paper,some practicalexamples in mechanics are given.     

ON THE SINGULAR PERTURBATION OF A NONLINEAR ORDINARY DIFFERENTIAL EQUATION WITH TWO PARAMETERS

In this paper,the method of differential inequalities has been applied to study theboundary value problems of nonlinear ordinary differential equation with two parameters.The asymptotic solutions have been found and the remainders have been estimated.     

THE NECESSARY AND SUFFICIENT CONDITION OF UNIFORMLY CONVERGENT DIFFERENCE SCHEMES FOR THE ELLIPTIC-PARABOLIC PARTIAL DIFFERENTIAL EQUATION WITH A SMALL PARAMETER

This paper studies the necessary and sufficient condition of uniformly convergent difference scheme for the elliptic-parabolic partial differential equation with a small parameter.     

THE LARGE DEFLECTION ON PROBLEM OF CIRCULAR PLATE ON ELASTIC FOUNDATION AND IN CONJUNCTION WITH LINEAR ELASTIC STRUCTURE

This paper deals with the axisymmetrical deformation of the circular plate in largedeflection,which is on elastic foundation and in conjunction with a certain linear elasticstructure.The governing integral equations are established by the method of mixedboundary condition I and the simplified form is given.The pertrubation method is used toobtain the solutions and an example of the composite structure made up of a circular plateand a cylindrical shell is presented.     

ON SOLUTIONS OF BACKWARD STOCHASTIC DIFFERENTIAL EQUATIONS WITH JUMPS, WITH UNBOUNDED STOPPING TIMES AS TERMINAL AND WITH NON-LIPSCHITZ COEFFICIENTS, AND PROBABILISTIC INTERPRETATION OF QUASI-LINEAR ELLIPTIC TYPE INTEGRO- DIFFERENTIAL EQUATIO

Ｉｔ’ｓｗｅｌｌ＿ｋｎｏｗｎｔｈａｔｔｈｅｓｏｌｕｔｉｏｎｓｏｆｂａｃｋｗａｒｄｓｔｏｃｈａｓｔｉｃｄｉｆｆｅｒｅｎｔｉａｌｅｑｕａｔｉｏｎｓ(ＢＳＤＥｓ)ｐｌａｙａｎｉｍｐｏｒｔａｎｔｒｏｌｅｉｎｔｈｅｆｉｎａｎｃｉａｌｍａｒｋｅｔ(ＳｅｅＲｅｆ.[1]).ＷｉｔｈｕｎｂｏｕｎｄｅｄｓｔｏｐｐｉｎｇｔｉｍｅｓτａｓｔｅｒｍｉｎａｌｓｕｎｄｅｒｔｈｅＬｉｐｓｃｈｉｔｚｃｏｎｄｉｔｉｏｎｓａｎｄｃｏｎｄｉｔｉｏｎｔｈａｔｔｅｒｍｉｎａｌｓｓａｔｉｓｆｙＥ｜ξ｜2ｅＫ(τ∧Ｔ)≤ｃ0<∞,0≤Ｔ<∞ｏｒξ=0,Ｒｅｆｓ…     

New nonautonomous combined multi-wave solutions for ( $$\varvec{2+1}$$ 2 + 1 )-dimensional variable coefficients KdV equation

Nonlinear Dynamics - A variety of new types of nonautonomous combined multi-wave solutions of the ( $$2+1$$ )-dimensional variable coefficients KdV equation is derived by means of the generalized...