The Existence Of Solution Of Boundary Value Problem For Third Order Ordinary Differential Equations

The ordinary differential equation is an ancient old but important branch in the mathematics, it have the extensive application in natural science and the engineering techniques.The ordinary differential equation boundary value problem has extremely abundant headspring in the classic mechanics and science of electricities, it is the importance of the ordinary differential equation course to constitute one of the parts.After the year of 1893 Picard usage iteration method discussion two-point boundary value problem of nonlinear second order the ordinary differential equation existence and unique. The ordinary differential equation of the boundary value problem has got the booming developmented. Although the ordinary differential equation of the boundary value problem ( such as boundary value problem of Dirichlet, boundary value problem of Neumann, boundary value problem of Robin, boundary value problem of Sturm- Liouville and the period boundary value problem etc.) already drive thorough but extensive research, is still one of a little bit hot problems of the differential equation course research now.Currently the concerning the ordinary differential equation research of nonlinear problem obtains the graveness to make progress.The Gupta started study two ranks in 1992 not the existence of the line ordinary differential equation of third boundary value problem solution. So-called" not partial problem" mean that the ordinary differential equation is settled to solve the problem to solve the condition to not only depend on to carry to order in the interval in the equation of take the value, but also depend on certainly in solution in the interval interior of a little bit some up of take the value.The research of this class problem also has the important progress:On the other hand, built up many existence results to the not partial resonance problem of the not partial non- resonance problem sum;On the other hand, in ordering boundary value problem more just solve research of exist sex problem, found out to settle superior condition that the solution parameter should satisfy.Because not partial problem correspondence often the general right and wrong of differential operator is symmetry, so the research of this class problem still has many problems to want to do.This text is main the class of three point nonlinear differential equation boundary value problem solution carries on the discussion.Near a period, nonlinear ordinary differential equation boundary value problem is extensively pay attention to.But few people rank study a little bit much more opposite, also having a lot of article researches the concerning the differential equation of higher order boundary value problem.But is a little bit opposite and little to the research of the odd integer rank equation, this is because of the Green function dissymmetry of the odd integer rank equation, and nonexistent homologous conjugate equation.Because three point of the differential equations have the extensive application in the research of the courses, such as astronomy and fluid mechanics...etc. because of it, already having numerous cultural heritages to do the study.This text chapter 1 mainly said some articles all to three researches of the rank differential equation boundary value problems, in chapter 2 and chapter 3s, then from the structure angle of the new function, to the function in the boundary value problem put forward another one class of constraint condition, the method that makes use of the principle and top and bottoms solution acquires the existence of understanding, expanding some cultural heritages in of correspond the conclusion.I discusses three point of nonlinear ordinary differential equation boundary value problem in the chapter two: Establish the function h : [0 ,1]×R~3→R satisfies the Carath eodory condition:( I) (?)( u , v,w)∈R~3, h (t ,u,v,w)about t∈[0 ,1] can measure; ( Ii) a. e.t∈[0 ,1], h (t ,u,v,w) concerning (u ,v,w)∈R~3 the consecution; ( Iii)make a. e.t∈[0 ,1] and arbitrarily (u ,v,w)∈R~3, u~2 + v~2+w~2≤r~2,satisfied h (t ,u,v,w)≤R. And the existence functionα(t),β(t),γ(t),δ(t)∈L~1 [0 ,1],make to t∈[0,1] and each (u,v,w)∈R~3,all have Establish h(t,u,v,w)≤α(t)u+β(t)v+γ(t)w+δ(t).While then being :the problem exists a solution at least. It mainly solution that begs the not strange equation, through a method of variation of constant,then make use of the principle Leray? Schauder certificate operator KN : C~2[0 ,1]→C~2[0 ,1] exist the fixed point,prove that the theorem say is right from here . For the nonlinear differential equation boundary value problem because of its deep research background, still have many works to want to do.