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1.
在一对上-下解和下-上解存在的条件下,研究了一类二阶耦合积分边值问题{-x"=f_1(t,x,y,x"),-y"=f_2(t,x,y,y'),t∈[0,1],x(0)=y(0)=0,x(1)+∫_0~1y(t)dA(t)=0,y(1)+∫_0~1x(t)dB(t)=0}解的存在性,其中f_1,f_2∈C([0,1]×R~3,R).  相似文献   

2.
一类二阶常微分方程无穷多点边值问题解的存在性   总被引:1,自引:0,他引:1  
运用Leray-Schauder原理在.f满足至多线性增长的条件下研究了无穷多点边值问题{y'(x)=f(x,y(x),y'(x))+e(x),0x1y(0)=0,y(1)=∞∑i=1a_iy(ξ_i)解的存在性.  相似文献   

3.
本文应用上下解方法研究了边值问题εy″=f(t,y,ε),L(y(0),y′(0),ε)=0,R(y(1),y′(1),ε)=0(含一般的Robin问题)的解的存在性,唯一性和估计.  相似文献   

4.
本文研究了奇异摄动边值问题:εy″=f(t,y,ε),y(0)=ξ(ε),y(1)=η(ε),其中ε是一个正小参数.在条件fy(0,y,0)≥m_0(>0),fy(1,y,0)≥m_0和fy(t,y,ε)≥0之下.我们证明了解的存在唯一性,并给出了解的一致有效渐近展开式,从而改进了已有的结果.  相似文献   

5.
利用压缩映射原理讨论了边值问题y(4)(t)=f(t,y,y′,y,″y′″),y(a)=y(b)=0,y″(a)=y″(b)=0解的存在唯一性问题,得出了当f满足Lipschitz条件时边值问题解的存在唯一性定理,并证明了当f为半线性f(t,y)时结论是最优的.同时给出了一个改进的Picard迭代误差公式,此公式保证了端点处误差为零.  相似文献   

6.
莫嘉琪 《应用数学》1994,7(1):65-69
本文研究了非线性边值问题: εy″-f(x,y,y′)=0,0相似文献   

7.
以二阶的情形讨论了Poincaré差分方程y(n m) (a1 p1(m))y(n m-1) … (an pn(m)y(m)=0当其常系数部分x(n m) a1x(n m-1) … anx(m)=0的特征方程有相同的根时,解的渐近性质,通过不动点方法给出了Poincaré差分方程的解渐近于其常系数方程解的条件,并给出了渐近式高阶项的估计。  相似文献   

8.
非齐次边值条件下一类静态梁方程非负解的存在性   总被引:1,自引:1,他引:0  
运用Schauder不动点定理,在非齐次边值条件,讨论带导数项的一端简单支撑另一端滑动的静态梁方程y^(4)(x)=f(x,y(x),y′(x),y″,y^(3)(x)),x∈[0,1] y(0)=a,y′(1)=b,y″(0)=c,y^(3)(1)=d非负解的存在性,其中a≥0,b≥0,c≤0,d≤0。假定f在零点次线性增长,在无穷远点超线性增长,则上述非齐次边值问题当max{a,b,-c,-d}充分小时有非负解存在,当max{a,b,-c,-d}充分大时无非负解存在。  相似文献   

9.
具p-Laplacian算子型奇异方程组边值问题正解的存在性   总被引:10,自引:0,他引:10  
刘斌 《数学学报》2005,48(1):35-50
本文讨论了一类具p-Laplacian算子型奇导方程组边值问题(φp(x'))'+α1(t),f(x(t),y(t))=0,(φp(y'))'+α2(t)g(x(t),y(t))=0,x(0)-β1x'(0)=0,x(1)+δ1x'(1)=0,y(0)-β2Y'(0)=0,y(1)+δ2y'(1)=0正解的存在性,其中φp(x)=|x|p-2x,p>1.通过使用不动点指数定理,在适当的条件下,建立了这类奇异方程组边值问题存在一个或者多个正解的充分条件.这些结果能用来研究椭圆型方程组边值问题径向对称解的存在性.  相似文献   

10.
本文考虑二阶线微分方程 y″+t~2f(t)g(y)=0 (1) 的可积性,设G(y)=integral from n=0 to y(g(s)ds),我们证明了在一定的条件下,方程(1)的一切解满足估计: integral from n=t_0 to ∞((G(y(t))/f(t))dt)〈+∞。  相似文献   

11.
本文在L^1空间中讨论了一类多群流算子的谱性质。证明了该算子的谱由可数多个具有有限代数重数的特征值组成,并且给出了特征子空间和投影算子的表示。因此,在多群意义下解决了第七届国际迁移理论会议上提出的一个公开问题。  相似文献   

12.
方程u_(tt)=u_(xxt)+f(u_x)_x初边值问题的差分法   总被引:10,自引:0,他引:10  
The finite difference method is considered for the followinginitial-boundary-value problem: arrayllutt=uxxt+f(ux)x, & (x,t) QT, u(x,0) =(x), & x [0,1], ut(x,0) = (x), & x [0,1], u(0,t) =u(1,t) =0, & t [0,T],array. where f(s),(x) and (x) are given functions;QT=[0,1] [0,T]. The convergence of the finite difference schemesis verified by discrete functional analysis methods and prior estimationtechniques.  相似文献   

13.
We study the initial-boundary value problem of the Navier-Stokes equations for incompressible fluids in a general domain in R^n with compact and smooth boundary, subject to the kinematic and vorticity boundary conditions on the non-flat boundary. We observe that, under the nonhomogeneous boundary conditions, the pressure p can be still recovered by solving the Neumann problem for the Poisson equation. Then we establish the well-posedness of the unsteady Stokes equations and employ the solution to reduce our initial-boundary value problem into an initial-boundary value problem with absolute boundary conditions. Based on this, we first establish the well-posedness for an appropriate local linearized problem with the absolute boundary conditions and the initial condition (without the incompressibility condition), which establishes a velocity mapping. Then we develop apriori estimates for the velocity mapping, especially involving the Sobolev norm for the time-derivative of the mapping to deal with the complicated boundary conditions, which leads to the existence of the fixed point of the mapping and the existence of solutions to our initial-boundary value problem. Finally, we establish that, when the viscosity coefficient tends zero, the strong solutions of the initial-boundary value problem in R^n(n ≥ 3) with nonhomogeneous vorticity boundary condition converge in L^2 to the corresponding Euler equations satisfying the kinematic condition.  相似文献   

14.
ONTHEEXISTENCEANDUNIQUENESSOFTHESOLUTIONTOTHENAVIER-STOKESEQUATIONSTangXianjiang(Dept.ofMath.,Sichuanuniversity,Chengdu610064...  相似文献   

15.
We consider the numerical solution of the free boundary Bernoulli problem by employing level set formulations. Using a perturbation technique, we derive a second order method that leads to a fast iteration solver. The iteration procedure is adapted in order to work in the case of topology changes. Various numerical experiments confirm the efficiency of the derived numerical method.  相似文献   

16.
马璇 《数学杂志》2004,24(3):259-262
考虑热传导方程的初边值问题的解。当初值与边值“不相容”时。由于热传导方程的特性这个解可以在很短时间内变得光滑。并形成一个边界层,本文将通过上、下解的控制给出解在边界附近变化的渐进行为.  相似文献   

17.
1.IntroductionManyproblemsarisinginfluidmechanicsaregiveninanunboundeddomain,suchasfluidflowaroundobstacles.Whencomputingthenumericalsolutionsoftheseproblems,oneoftenintroducesartificialboundariesandsetsupaxtificialboundaryconditionsonthem.Thentheoriginal…  相似文献   

18.
本文讨论了一维Stefan-Signorini问题的均匀化.利用一个关于未知函数的变换,将原问题转化为一个等价问题,然后利用一些估计和分析技巧对后者进行均匀化.这部分地回答J.R.Rodrisues提出的一个问题.  相似文献   

19.
The boundary element approximation of the parabolic variational inequalities of the second kind is discussed. First, the parabolic variational inequalities of the second kind can be reduced to an elliptic variational inequality by using semidiscretization and implicit method in time; then the existence and uniqueness for the solution of nonlinear non-differentiable mixed variational inequality is discussed. Its corresponding mixed boundary variational inequality and the existence and uniqueness of its solution are yielded. This provides the theoretical basis for using boundary element method to solve the mixed vuriational inequality.  相似文献   

20.
In this paper, a new collocation BEM for the Robin boundary value problem of the conductivity equation ▽(γ▽u) = 0 is discussed, where the 7 is a piecewise constant function. By the integral representation formula of the solution of the conductivity equation on the boundary and interface, the boundary integral equations are obtained. We discuss the properties of these integral equations and propose a collocation method for solving these boundary integral equations. Both the theoretical analysis and the error analysis are presented and a numerical example is given.  相似文献   

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