SINGULAR PERTURBATION OF ROBIN BOUNDARY VALUE PROBLEM FOR THIRD ORDER NONLINEAR SYSTEM WITH BOUNDARY PERTURBATION

ＳＩＮＧＵＬＡＲＰＥＲＴＵＲＢＡＴＩＯＮＯＦＲＯＢＩＮＢＯＵＮＤＡＲＹＶＡＬＵＥＰＲＯＢＬＥＭＦＯＲＴＨＩＲＤＯＲＤＥＲＮＯＮＬＩＮＥＡＲＳＹＳＴＥＭＷＩＴＨＢＯＵＮＤＡＲＹＰＥＲＴＵＲＢＡＴＩＯＮ（黄晓秋）福建师范大学福清分校，邮编：３５０３００Ｈ...     

SINGULAR PERTURBATION OF THIRD ORDER NONLINEAR BOUNDARY VALUE PROBLEM WITH TWO TURNING POINTS

1IntroductionManyauthorshavedealtwiththeboundaryvalueproblemsofsecondorthirdorderdifferentialequationwithaturningpoint[l-5],butthatwithtwoormoreturningpointsisscarcelydiscussed.ThispaperconcernsthefollowingboundaryvalueproblemwhereE>0isasmallparameter,0,I…     

SINGULAR PERTURBATION OF BOUNDARY VALUE PROBLEM FOR NONLINEAR HIGHER ORDER ORDINARY DIFFERENTIAL EQUATIONS INVOLVING TWO SMALL PARAMETERS

The singularly perturbed boundary value problem for nonlinear higher order ordinary differential equation involving two small parameters has been considered. Under appropriate assumptions, for the three cases:ε/μ2→0(μ→0),μ2/ε→0 (ε→0) andε=μ2, the uniformly valid asymptotic solution is obtained by using the expansion method of two small parameters and the theory of differential inequality.     

SINGULAR PERTURBATION OF BOUNDARY VALUE PROBLEM FOR QUASILINEAR HIGHER ORDINARY DIFFERENTIAL EQUATION

In this paper we study the singular perturbation of boundary value problems with perturbations both in the operater and in the interval ends. So as to prove the existence and uniqueness of solution of perturbed problem, to establish the asymptotic expression involving three parameters. Thus, the iterative equation of finding the asymptotic solution is derived and the estimation of the remainder term is given out. We extend results of [1]—[5].     

SINGULAR PERTURBATION OF THREE-POINT BOUNDARY VALUE PROBLEM FOR THIRD ORDER DIFFERENTIAL EQUATIONS

In this paper, by the theory of differential inequalities, we study the existence and uniqueness of the solution to the three-point boundary value problem for third order differential equations. Furthermore we study the singular perturbation of three-point boundary value problem to third order quasilinear differential equations, construct the higher order asymptotic solution and get the error estimate of asymptotic solution and perturbed solution.     

SINGULAR PERTURBATIONS OF A HIGHER-ORDER SCALAR NONLINEAR BOUNDARY VALUE PROBLEM

1IntroductionInthispaper,weconsiderthesingularperturbationsofthefollowinghigher-ordernonlinearboundaryvalueproblemwheree>0isasmallparameter,n22,yER;thegivendataquantitiesHIandHZare(n--2)-d~sionaland2-dimensionalrealvector-valuedfunctions,respectively.ThesendlinearboundaryvalueproblemcanbewrittenintheformOf(1.1)-(1.3).Thesingularperturbationsfortheproblem(1.4)havebeenstudiedbymanyauthors(of.e.g.[1]-[3]).Thesestudieshavebeenmacebythemethodsofthedifferentialinequalitytechniques.However,itseem…     

EXISTENCE FOR A TWO POINT BOUNDARY VALUE PROBLEM ARISING IN ELECTRODIFFUSION

In this paper, we consider a two point boundary value problem of the formy″=f(x, y, y′, y(0), y(1));y′(0)=0=y′(1),where f: [0,1]×R~(4n)→R~n is continuous.     

POSITIVE SOLUTIONS OF BOUNDARY VALUE PROBLEM FOR A SYSTEM OF NONLINEAR ORDINARY DIFFERENTIAL EQUATIONS

By using topological method, we study a class of boundary value problem for a system of nonlinear ordinary differential equations. Under suitable conditions, we prove the existence of positive solution of the problem.     

THE SINGULARLY PERTURBED BOUNDARY VALUE PROBLEM OF NONLINEAR INTEGRO-DIFFERENTIAL SYSTEM

In this paper, using the differential inequality and singularly perturbed theory, the singularly perturbed boundary value problems for nonlinear integro-differential system has been studied. Under some appropriate assumptions, the existence of solution has been proved and the uniform validness of the asymptotic expansions for arbitrary nth-order have been obtained simply and conveniently.     

POSITIVE SOLUTIONS FOR SINGULAR BOUNDARY VALUE PROBLEM OF SECOND ORDER

Some results of existence of positive solutions for singular boundary value problems{-u"(t)=p(t)f(u(t)), t∈(0,1), u(0)=u(1)=0are given, where the function p(t) may be singular at t = 0, 1.     

TWO POSITIVE SOLUTIONS FOR A CLASS OF SINGULAR BOUNDARY VALUE PROBLEMS

An existence theorem of two positive solutions of the singular BVP1/(p(t))(p(t)y′(t))′+λα(t)f(y(t))=0,t∈(0,1),αy(0)-βp(t)y′(t)=0=γy(1)+δp(t)y′(t)was established by using topological degree theory.     

MULTIPLE POSITIVE SOLUTIONS OF BOUNDARY VALUE PROBLEM FOR A SYSTEM OF NONLINEAR THIRD ORDER DIFFERENTIAL EQUATIONS

This paper is concerned with the boundary value problem for a system of nonlinear third order differential equations. Under some suitable conditions, the existence and multiplicity of the positive solutions are established by using abstract fixed-point theorems.     

POSITIVE SOLUTION FOR NONLINEAR SINGULAR BOUNDARY VALUE PROBLEMS

Under suitable conditions on f(·,u), it is shown that the two-point boundaryvalue problem((u'))' + λq(t)f(u) = 0in (0, 1),u(0) = u(1) = 0,has two positive solution or at least one positive solution for λ in a compatibleinterval.     

POSITIVE SOLUTIONS OF SINGULAR THREE-POINT BOUNDARY VALUE PROBLEM

The existence of the positive solutions of a certain second order singular differential equation is studied. Our result is based on fixed-point theorem of cone expansion and compression.     

ASYMPTOTIC ESTIMatION OF ROBIN BOUNDARY VALUE PROBLEM FOR THIRD NONLINEAR EQUATION

1IntroductionThepreviousworks,forexample,theref',renccsll,21,havedis(fusscdthoboundaryvalueproblemswitlltwopointboundarycondition.Inthispaper,weconsiderRobinbonn(laryvalueproblemofthefornltheexistenceandasymptoticestimationofsolutionareestablished.Where2…     

INITIAL VALUE PROBLEM FOR A CLASS OF NONLINEAR PARABOLIC SYSTEM OF FOURTH-ORDER

In this paper, the periodic boundary problem and the initial value problem for the nonlinear system of parabolic type u_1=-A(x, t)u_(x4)+B(x, t)u_(x2)+(g(u))_(x2)+(grad h(u))_x+f(u)are studied, where u(x, t)=(u_1(x, t).…, u_J(x, t) is a J-dimensional unknown vector valued function, f(u) and g(u) are the J-dimensional vector valued function of u(x, t), h(u) is a scalar function of u, A(x, t) and B(x, t) are J×J matrices of functions. The existent, uniqueness and regularities of the generalized global solution and classical global solution of the problems are proved. When J=1, h(u)=0, g(u)=au~3, A=a_1, B=a_2, where a_1, a_2 a are constants, the system is a generalized diffusion model equation in population problem.     

ON UNIFORMLY VALID ESTIMATE OF SOLUTIONS TO SINGULAR PERTURBATION ROBIN BOUNDARY VALUE PROBLEM

In this paper we study the Robin boundary value problem with a small parameterεy″=f(t, y, ω(ε)y′, ε),a_0y(0) +b_0y′(0)=(ε), a_1y(1)+b_1y′(1)=η(ε),where the function ω(ε) is continuous on ε≥0 with ω(0)=0. Assuming all known functions are suitably smooth, f satisfies Nagumo's condition, f_y>0, a_t~2-b_t~2≠0, (-1)~ia_ib_i≤0 (i=0, 1) and the reduced equation 0=f(t, y, 0, 0) has a solution y(t) (0≤t≤1), we prove the existence and the uniqueness of the solution for the boundary value problem and givo an asymptotic expansion of the solution in the power ε~(1/2) which is uniformly valid on 0≤t≤1.     

A FOUR-POINT BOUNDARY VALUE PROBLEM FOR NONLINEAR EQUATION

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

NONLINEAR INITIAL-BOUNDARY VALUE PROBLEM FOR QUASILINEAR HYPERBOLIC SYSTEM

Consider the nonlinear inltial-boundary value problem for quasilinear hyperbolicsystem:Let k≥2[n/2] 6,(F,g)∈ H~k(R_ ;Ω)×H~k(R_ ;Ω),and their traces at t=0 are zeroup to the order k-1.If for u=0,the problem(*)at t=0 is a Kreiss hyperbolic system,and the boundaryconditions satisfy the uniformly Lopatinsky criteria,then there exists a T>0 such that(*)has a unique H~k soluton in(0,T).In the Appendix,for symmetric hyperbolic systems,a comparison between theuniformly Lopatinsky condition and the stable admissible condition is given.