SOLVABILITY OF M-POINT BOUNDARY VALUE PROBLEMS FOR SECOND ORDER ORDINARY DIFFERENTIAL EQUATIONS

1IntroductionRecentlytmultiplepointsboundaryvalueproblemsforordinarydifferentialequationsarcextensivelystudied,see[1-4].Inthispapertweconsiderthesolvabilityofthefollowingsecondorderordinarydifferentialequationwithm-pointboundaryvalueconditionswhere,fsatisfiesCaratheodory'sconditions,al,...,am--2havethesamesign,fi,...,(.--2E(0,1),eEL'(0,1),andthesignZdenotesthesumZ7=i'.InthecaseOfa=Zal/1,theproblem(1.1),(1.2)wasstudiedin[1],bymeansoftheLeray-Schaudercontinuationtheorem,whileinthecaseofor51a…     

ON WELL-CONDITIONED BOUNDARY VALUE PROBLEMS FOR SYSTEMS OF SECOND ORDER DIFFERENCE EQUATIONS

In this paper well-conditioning of boundary value problems for systems of second order difference equa-tions is studied.First,a sufficient condition for the existence of a unique bounded solution (for large enough number of steps) of an associated homogeneous system is given.Finally,a sufficient condition for well-condi-tioning,intrinsically related to the problem data is proposed.     

SOME BOUNDARY VALUE PROBLEMS FOR NONLINEAR DEGENERATE ELLIPTIC EQUATIONS OF SECOND ORDER

The present article deals with some boundary value problems for nonlinear elliptic equations with degenerate rank 0 including the oblique derivative problem.Firstly the formulation and estimates of solutions of the oblique derivative problem are given, and then by the above estimates and the method of parameter extension,the existence of solutions of the above problem is proved.In this article,the complex analytic method is used,namely the corresponding problem for degenerate elliptic complex equations of first order is firstly discussed,afterwards the above problem for the degenerate elliptic equations of second order is solved.     

BOUNDARY VALUE PROBLEMS FOR SECOND ORDER MIXED-TYPE FUNCTIONAL DIFFERENTIAL EQUATIONS

We use the topological degree method to deal with the generalized Sturm-Liouville boundary value problem (BVP) for second order mixed-type functional differential equation x(t)=f(t,xt,xt), 0≤t≤T. Existence principle and theorem for solutions of the BVP are obtained.     

EXISTENCE OF SOLUTIONS OF STURM-LIOUVILLE BOUNDARY VALUE PROBLEMS FOR NONLINEAR SECOND ORDER IMPULSIVE DIFFERENTIAL EQUATIONS IN BANACH SPACES

In this paper, the fixed point theorem is applied to investigate the existence of solutions of Sturm-Liouville boundary value problems for nonlinear second order impulsive differential equations in Banaeh spaces.     

SINGULAR PERTURBATIONS OF BOUNDARY VALUE PROBLEMS FOR THIRD ORDER NONLINEAR ORDINARY DIFFERENTIAL EQUATIONS

In this paper we obtain some results about the convergence of aolutions of the boundary value problems of the third order nonlinear ordinary differential equation with a small parameter ε>0: (i=0, 1, 2) to a solution of their reduced problem as ε→0, hero z=ψ(t, x, y) is a root of the equation f(t, x, y, z, 0)=0, and about the existence of solutions of the reduced problem. In addition, under certain conditions we prove the existence of solutions of the boundary value problems (1), (2_i) (i=1, 2), and give their asymptotic estimations.     

EXISTENCE OF SOLUTIONS TO NONLINEAR TWO POINTS BOUNDARY VALUE PROBLEMS OF SECOND ORDER ORDINARY DIFFERENTIAL EQUATIONS

In this paper, we obtain some criteria for the existence of solutions to nonli-near two-point boundary value problems by constructing some Liapunov func-tions, and we give some examples for our results to this problem in the end.     

EXISTENCE OF SOLUTIONS OF NONLINEAR TWO AND THREE-POINT BOUNDARY VALUE PROBLEMS FOR FOURTH ORDER NONLINEAR DIFFERENTIAL EQUATIONS

In this paper, the two and three-point boundsry problems (with nonlinear boundary conditions)for the genaral noniinear equations of fourth order are discussed.We have set some grups of the assurnpion coditions and proved the existence of solutins for corresponding boundary value problems under these conditons.     

BOUNDARY VALUE PROBLEMS FOR THIRD ORDER DIFFERENTIAL EQUATIONS

ＢＯＵＮＤＡＲＹＶＡＬＵＥＰＲＯＢＬＥＭＳＦＯＲＴＨＩＲＤＯＲＤＥＲＤＩＦＦＥＲＥＮＴＩＡＬＥＱＵＡＴＩＯＮＳ王金枝内蒙古大学，邮编：０１００２１ＢＯＵＮＤＡＲＹＶＡＬＵＥＰＲＯＢＬＥＭＳＦＯＲＴＨＩＲＤＯＲＤＥＲＤＩＦＦＥＲＥＮＴＩＡＬＥＱＵＡＴＩ...     

STURM COMPARISON THEOREM OF SOLUTION FOR SECOND ORDER NONLINEAR DIFFERENTIAL EQUATIONS

In this paper, we establish some differential identities and obtain some Sturm comparison theorems for the second order nonlinear differential equation by using them.and generalize some classicial Sturm comparison theorems.     

BOUNDARY VALUE PROBLEMS FOR SYSTEMS OF NONLINEAR SECOND ORDER DIFFERENTIAL DFFERENCE EQUATIONS

The author studies the boundary value problems for systems of nonlinear second order differential difference equations and adopts a new-type Nagumo condition,in whichthe control function is a vector-valued function of several variables and which can guarantee simultaneoulsy and easily finding a priori bounds of each component of the derivatives of the solutions,Under this new-type Nagumo condition the existence results of solutions are proved by means of differential inequality technique.     

四阶非线性常微分方程非线性两点边值问题解的存在唯一性

本文利用Ｂｏｌｚａｎｏ定理，给出了四阶非线性常微微分方程具有非线性边界条件的两点边值问题（１）（２）２，（１）（２）３存在解与存在唯一解的一般性结果，并将所得结果应用于Ｌｉｐｓｃｈｉｚ方程，对Ｌｉｐｓｃｈｉｔｚ方程满足边界条件（２）２，（２）３的边值问题给出了存在解与存在唯一解的具体的充分条件。     

A CLASS OF NONLOCAL SIINGULARLY PERTURBED NONLINEAR BOUNDARY VALUE PROBLEMS

Considerthesingularlyperturbednonlinearproblemfory~(y,?'...7/.)"oftheformwhereTy=(Tlyll'..5Tny.)'(Tdenotestransposition)whileEisasmallpositiveparameter,f=(fi,...?fn)",g=(gi,...,g.)',A=(Al,''tA.)',B=(BI,'',B.)'anda20,b20,a 5>0.Manyant,horssuchasHowes[1],…     

一类两点边值问题的正解个数

本文讨论边值问题y'+λ(yp+μp+yp)=0,y(-1)=y(1)=0,其中λ>0是正参数,μ≥0.对(1-p)(1-q)>0的情形得出了正解的存在唯一性.对(1-p)(1-q)<0的情形,其主要结论是:若p>1>q>-(25+23p)/(23+25p),μ≥0,则存在λ*>0,使得当0<λ<λ*时,此边值问题恰好存在两个正解,当λ=λ*时,存在唯一正解,当λ>λ*时,不存在正解.     

A FOUR-POINT BOUNDARY VALUE PROBLEM FOR NONLINEAR EQUATION

1IntroductionThemethodofupperandlowersolutionshasbecomeastandardtoolforstudyingthesolvabilityoftwo-pointboundaryvalllcproblemsassociatedwitllsecond-ordernonlineardifferentialequations.Inrecent,years,Rachunkovd[1,2,3]studiedthefour--pointboundaryvalueprobl…     

二阶奇异泛函微分方程的两点边值问题

本文研究具有Ｒｏｂｉｎ边界条件的二阶奇异泛函微分方程组Ａ（ｔ,ｘ,ｘ）ｘ＝ｆ（ｔ,ｘｔ,ｘｔ）的两点边值问题,给出该两点边值问题的两个解的先验估计定理和一个解的存在定理．     

二阶离散边值问题的一个存在性定理

作者利用监界点理论中的山路引理研究了一类非线性二阶差分方程边值问题解的存在性,获得了该边值问题有解的一个充分条件.     

COMPARISON THEOREMS TO BOUNDARY VALUE PROBLEMS FOR ORDINARY DIFFERENTIAL EQUATIONS

ＣＯＭＰＡＲＩＳＯＮＴＨＥＯＲＥＭＳＴＯＢＯＵＮＤＡＲＹＶＡＬＵＥＰＲＯＢＬＥＭＳＦＯＲＯＲＤＩＮＡＲＹＤＩＦＦＥＲＥＮＴＩＡＬＥＱＵＡＴＩＯＮＳ￥ＬＩＹＯＮＧ；ＷＡＮＧＨＵＡＩＺＨＯＮＧＡｂｓｔｒａｃｔ：Ａｕｎｉｆｉｅｄａｐｐｒｏａｃｈｉｓｇｉｖｅ...     

THE SINGULARLY PERTURBED NONLINEAR BOUNDARY VALUE PROBLEMS

§ 1　 IntroductionA class of singularly perturbed boundary value problems were studied by Mo[1～ 6] .Now we consider the following singularly perturbed nonlinear boundary value problem ofthe formεd2 ydx2 =f(x,y,y′) ,　 0 相似文献   

A KIND OF SINGULARLY PERTURBED BOUNDARY VALUE PROBLEM FOR NONLINEAR VOLTERRA FUNCTIONAL DIFFERENTIAL EQUATIONS

§ 1　IntroductionSince 1 970 the perturbed boundary value problems for functional differential equationshave been derived in many fields,such as biology,physics,optimal control and e-conomies[1 ] .Some works on studying it have appeared,for example references[2～ 6] .Inthis paper,we study a kind of singularly perturbed boundary value problems for Volterrafunctional differential equations:εx″(t) =f(t,x(t) ,[Tx] (t) ,x(t-τ) ,x′(t) ,ε) ,t∈ (0 ,1 ) ,(1 )x(t) =φ(t,ε) ,t∈ [-τ,0 ] ,ax(1 )…