SINGULAR PERTURBATIONS FOR A CLASS OF BOUNDARY VALUE PROBLEMS OF HIGHER ORDER NONLINEAR DIFFERENTIAL EQUATIONS

ＳＩＮＧＵＬＡＲ　ＰＥＲＴＵＲＢＡＴＩＯＮＳ　ＦＯＲ　Ａ　ＣＬＡＳＳ　ＯＦ　ＢＯＵＮＤＡＲＹ　ＶＡＬＵＥ　ＰＲＯＢＬＥＭＳ　ＯＦ　ＨＩＧＨＥＲ　ＯＲＤＥＲ　ＮＯＮＬＩＮＥＡＲ　ＤＩＦＦＥＲＥＮＴＩＡＬ　ＥＱＵＡＴＩＯＮＳＳｈｉＹｕａｎｉｎｇ（史玉明）...     

EXISTENCE THEOREMS OF EXTREMAL SOLUTIONS FOR A CLASS OF NONLINEAR INTEGRO－DIFFERENTIAL EQUATIONS

ＥＸＩＳＴＥＮＣＥＴＨＥＯＲＥＭＳＯＦＥＸＴＲＥＭＡＬＳＯＬＵＴＩＯＮＳＦＯＲＡＣＬＡＳＳＯＦＮＯＮＬＩＮＥＡＲＩＮＴＥＧＲＯ－ＤＩＦＦＥＲＥＮＴＩＡＬＥＱＵＡＴＩＯＮＳＳｏｎｇＧｕａｎｇｘｉｎｇ（宋光兴）（ＲｅｃｅｉｖｅｄＭａｙ４，１９９５；Ｃｏｍ...     

ON THE ASYMPTOTIC SOLUTIONS OF BOUNDARY VALUE PROBLEMS FOR A CLASS OF SYSTEMS OF NONLINEAR DIFFERENTIAL EQUATIONS (Ⅰ)

ＩｎｔｒｏｄｕｃｔｉｏｎＯｗｉｎｇｔｏｔｈｅｆａｃｔｔｈａｔｔｈｅｓｏｌｕｔｉｏｎｓｏｆｔｈｅＤｉｒｉｃｈｌｅｔｐｒｏｂｌｅｍｓｆｏｒａｃｌａｓｓｏｆｓｙｓｔｅｍｓｏｆｄｉｆｆｅｒｅｎｔｉａｌｅｑｕａｔｉｏｎｓｏｆｔｈｅｆｏｒｍｕ″=ｖ ,εｖ″ ｆ(ｘ ,ｕ ,ｕ′)ｖ′ -ｇ(ｘ ,ｕ ,ｕ′)ｖ=0　　 ( 0 <ｘ <1,0 <ε 1) ,ｕ( 0 ;ε) =0 ,ｕ( 1;ε) =0 ,ｖ( 0 ;ε) =α ,ｖ( 1;ε) =β,( 1)ｈａｖｅｔｈｅｑｕａｌｉｔａｔｉｖｅｐｒｏｐｅｒｔｉｅｓｏｆｓｏｌｕｔｉｏｎｓｏｆａｍｏｒｅｃｏｍｐｌｉｃａｔｅｄｓｙｓｔｅ…     

FORCED OSCILLATIONS OF BOUNDARY VALUE PROBLEMS OF HIGHER ORDER FUNCTIONAL PARTIAL DIFFERENTIAL EQUATIONS

ＦＯＲＣＥＤＯＳＣＩＬＬＡＴＩＯＮＳＯＦＢＯＵＮＤＡＲＹＶＡＬＵＥＰＲＯＢＬＥＭＳＯＦＨＩＧＨＥＲＯＲＤＥＲＦＵＮＣＴＩＯＮＡＬＰＡＲＴＩＡＬＤＩＦＦＥＲＥＮＴＩＡＬＥＱＵＡＴＩＯＮＳＪｉｎＭｉｎｇＺｈｏｎｇ（靳明忠），ＤｏｎｇＹｉｎｇ（董莹），Ｌｉ...     

SINGULARLY PERTURBED BOUNDARY VALUE PROBLEMS FOR SEMI-LINEAR RETARDED DIFFERENTIAL EQUATIONS WITH NONLINEAR BOUNDARY CONDITIONS

IntroductionInthispaper,westudiedakindofboundaryvalueproblems (BVPs)forsemi_linearretardeddifferentialequationwithnonlinearboundarycondition :　　　　εx″(t) =f(t,x(t) ,x(t-ε) ,ε) ,　　t∈(0 ,1 ) ,(1 )　　　　x(t) =φ(t,ε) ,　t∈[-ε0 ,0 ] ,h(x(1 ) ,x′(1 ) ,ε) =A(ε) ,(2 )whereε>0isasmallparameterandε0 isasufficientlysmallpositiveconstant.ThereweremanyresultsofstudyingonsingularlyperturbedboundaryvalueproblemforretardeddifferentialequationinRefs.[1～5] .Butthosestudiespossessedanesse…     

PROPER SOLUTIONS AND LIMIT BOUNDARY VALUE PROBLEMS OF NONLINEAR SECOND-ORDER SYSTEMS OF DIFFERENTIAL EQUATIONS

For the system of differential equations(?)=r(t)v_1 (?)=-a(t)f(x)g(v)where a(t)>0,r(t)>0 for t≥t_0;f(x)>0 and is decreasing forx>0,g(y)>0,we give necessary and sufficient condition of a propersolution.a bounded proper solution or sotutions of two kinds of boundary value problems onan infinite interval [c,∞),c≥t_0.Several examples are given to illustrate the conditionsof these results.     

EXISTENCE OF SOLUTIONS OF THREE－POINT BOUNDARY VALUE PROBLEMS FOR NONLINEAR FOURTH ORDER DIFFERENTIAL EQUATION

ＥＸＩＳＴＥＮＣＥＯＦＳＯＬＵＴＩＯＮＳＯＦＴＨＲＥＥ－ＰＯＩＮＴＢＯＵＮＤＡＲＹＶＡＬＵＥＰＲＯＢＬＥＭＳＦＯＲＮＯＮＬＩＮＥＡＲＦＯＵＲＴＨＯＲＤＥＲＤＩＦＦＥＲＥＮＴＩＡＬＥＱＵＡＴＩＯＮ￥ＧａｏＹｏｎｇｘｉｎ（高永馨）（Ｄｅｐａｒｔｍｅｎｔｏ...     

BOUNDARY VALUE PROBLEMS FOR SECOND ORDER SINGULARLY PERTURBED DIFFERENTIAL EQUATIONS

In this paper the existence and uniqueness of solutions of boundary value problems εy″=f(t,y,ε) L(y(0),y′(0),ε) =0, R(y(1), y′(1),ε)=0(which contains the Robi's problem) is discussed by using the upper and lower solution. In addition, the asymptotic estimation of the solution is given us well.     

NONOSCILLATION RESULTS FOR A CLASS OF THIRD ORDER NONLINEAR DIFFERENTIAL EQUATIONS

ＩｎｔｒｏｄｕｃｔｉｏｎＦｉｎｄｉｎｇｓｕｆｆｉｃｉｅｎｔｃｏｎｄｉｔｉｏｎｓｆｏｒｎｏｎｏｓｃｉｌｌａｔｏｒｙｏｆｓｏｌｕｔｉｏｎｓｉｓａｐｒｏｂｌｅｍｏｆｇｅｎｅｒａｌｉｎｔｅｒｅｓｔｉｎｔｈｅｔｈｅｏｒｙｏｆｏｒｄｉｎａｒｙａｎｄｄｅｌａｙｄｉｆｆｅｒｅｎｔｉａｌｅｑｕａｔｉｏｎｓ.Ｉｎｔｈｉｓｗｏｒｋｗｅｃｏｎｓｉｄｅｒｄｄｓ σ(ｓ) ｄｄｓ ｒ(ｓ) ｄｘｄｓ +ｑ(ｓ) ｄｘｄｓβ +ｐ(ｓ)ｘα =ｆ(ｓ) ,(1)ｗｈｅｒｅσ ,ｒ,ｑ,ｐａｎｄｆａｒｅｒｅａｌ＿ｖａｌｕｅｄｃｏｎｔｉｎｕｏｕｓｆｕｎｃｔｉ…     

RESEARCH OF THE PERIODIC SOLUTION FOR A CLASS OF NONLINEAR DIFFERENTIAL EQUATIONS

ＲＥＳＥＡＲＣＨＯＦＴＨＥＰＥＲＩＯＤＩＣＳＯＬＵＴＩＯＮＦＯＲＡＣＬＡＳＳＯＦ　ＮＯＮＬＩＮＥＡＲＤＩＦＦＥＲＥＮＴＩＡＬＥＱＵＡＴＩＯＮＳＲＥＳＥＡＲＣＨＯＦＴＨＥＰＥＲＩＯＤＩＣＳＯＬＵＴＩＯＮＦＯＲＡＣＬＡＳＳＯＦＮＯＮＬＩＮＥＡＲＤＩＦＦＥ...     

Initial value problems for a class of nonlinear integro-partial differential equations

１ＰｒｏｂｌｅｍｓａｎｄＭａｉｎＲｅｓｕｌｔｓＩｎｔｈｉｓｐａｐｅｒ,ｗｅｓｔｕｄｙｔｈｅｎｏｎｌｉｎｅａｒｖｉｂｒａｔｉｏｎｓｏｆｉｎｆｉｎｉｔｅｒｏｄｓｗｉｔｈｖｉｓｃｏｅｌａｓｔｉｃｉｔｙ．Ｔｈｅｃｏｎｓｔｉｔｕｔｉｏｎｌａｗｏｆｔｈｅｒｏｄｓ...     

Initial value problem for a class of fourth-order nonlinear wave equations

In this paper, existence and uniqueness of the generalized global solution and the classical global solution to the initial value problem for a class of fourth-order nonlinear wave equations are studied in the fractional order Sobolev space using the contraction mapping principle and the extension theorem. The sufficient conditions for the blow up of the solution to the initial value problem are given.     

Oscillation of solutions for a class of nonlinear neutral parabolic differential equations boundary value problem

ＩｎｔｒｏｄｕｃｔｉｏｎＤｕｅｔｏｔｈｅａｃｃｕｒｅｎｃｅｏｆａｇｒｅａｔｄｅａｌｏｆｍａｔｈｅｍａｔｉｃｍｏｄｅｌｌｉｎｇｓｄｅｓｃｒｉｂｅｄｉｎｐａｒｔｉａｌｆｕｎｃｔｉｏｎａｌｄｉｆｆｅｒｅｎｔｉａｌｅｑｕａｔｉｏｎｓｉｎｔｈｅａｐｐｌｉｃａｔｉｏｎｆｉｅｌｄｓｏｆｍｅｃｈａｎｉｃｓａｎｄｃｏｎｔｒｏｌｔｈｅｏｒｙ[1],ｇｒｅａｔｉｎｔｅｒｅｓｔｗａｓａｒｏｕｓｅｄａｓｔｏｔｈｅｓｔｕｄｉｅｓｏｎｔｈｅｐｒｏｐｅｒｔｙｏｆｔｈｅｓｏｌｕｔｉｏｎｓｏｆｔｈｉｓｔｙｐｅｏｆｅｑｕａｔｉｏｎｓ.Ｇ…     

Boundary value problems for second order delay differential equations

In this paper,using a fixed point principle and existence principle given in[1],westudy the boundary value problems for second order differential equations.Some newexistence results are obtained.     

Solvability of a class of second-order quasilinear boundary value problems

The second-order quasilinear boundary value problems are considered when the nonlinear term is singular and the limit growth function at the infinite exists. With the introduction of the height function of the nonlinear term on a bounded set and the consideration of the integration of the height function, the existence of the solution is proven. The existence theorem shows that the problem has a solution if the integration of the limit growth function has an appropriate value.     

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

IntroductionThereweresomeresultsofstudyingonboundaryvalueproblemsforfunctionaldifferentialequation[1～6 ]byemployingthetoplolgicaldegreetheoryandsomefixedpointprinciplesinrecentyears.Buttheworktostudyboundaryvalueproblemsfordelaydifferentialequationwithsmallparameterbymeansofthetheoryofsingularperturbationrarelyappeared[7～11].Thereasonforitisthattheworktoconstructtheuppersolutionandlowersolutionforthecaseofdifferentialequationwithdelayisdifficult.Theauthorhasstudiedakindofboundaryvalueproblem…     

Strength differential effect and influence of strength criterion on burst pressure of thin-walled pipelines

In the framework of the finite deformation theory, the plastic collapse analysis of thin-walled pipes subjected to the internal pressure is conducted on the basis of the unified strength criterion (USC). An analytical solution of the burst pressure for pipes with capped ends is derived, which includes the strength differential effect and takes the influence of strength criterion on the burst pressure into account. In addition, a USC-based analytical solution of the burst pressure for end-opened pipes under the internal pressure is obtained. By discussion, it is found that for the end-capped pipes, the influence of different yield criteria and the strength differential effect on the burst pressure are significant, while for the end-opened pipes, the burst pressure is independent of the specific form of the strength criterion and strength difference in tension and compression.