共查询到20条相似文献,搜索用时 15 毫秒
1.
General existence criteria are presented for nonlinear singular boundary value problems. Our nonlinearity may be singular
in both the dependent and independent variable.
This revised version was published online in June 2006 with corrections to the Cover Date. 相似文献
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In this paper we examine existence of monotone approximations of solutions of singular boundary value problem -(p(x)y′(x))′=q(x)f(x,y,py′) for 0<x?b and limx→0+p(x)y′(x)=0,α1y(b)+β1p(b)y′(b)=γ1. Under quite general conditions on f(x,y,py′) we show that solution of the singular two point boundary value problem is unique. Here is allowed to have integrable singularity at x=0 and we do not assume . 相似文献
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This article introduces a new concept of upper and lower solutions and studies the existence and uniqueness of solutions of second-order three-point boundary value problems with upper and lower solutions in the reversed order. The sufficient conditions for the existence and uniqueness of solutions are obtained by using the monotone iterative method, meantime, the iterative sequence for solving a solution and its error estimate formula under the condition of unique solution are given. Some results of previous literature are extended and improved. A numerical example is also included to illustrate the effectiveness of the proposed results. 相似文献
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n阶非线性常微分方程两点及三点边值问题解的存在性的进一步结果 总被引:6,自引:0,他引:6
本文利用上、下解方法讨论了n阶非线性常微分方程y^(n)=f(t,y,y‘…,y^(n-1))满足下列非线性边界条件的边值问题解的存在性。 相似文献
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This paper presents new existence results for singular discrete boundary value problems. In particular our nonlinearity may be singular in its dependent variable and is allowed to change sign. 相似文献
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In this work, by using the fixed point index method, some existence results for positive solutions of certain three-point boundary value problems are obtained under a non-well-ordered upper and lower solution condition. 相似文献
8.
The aim of this paper is to show the existence of solutions of the n-dimensional diffraction problem for weakly coupled quasilinear elliptic reaction-diffusion system. The coefficients of the equations under consideration are allowed to be discontinuous. We extend the method of upper and lower solutions for reaction-diffusion equations with continuous coefficients to the elliptic diffraction problem. An application of these results is given to the steady-state problem of Lotka-Volterra cooperation model with two cooperating species. 相似文献
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In this paper, we discuss existence theorems in the presenceof upper and lower solutions as well as the method of quasilinearization(QSL) for general non-linear second-order singular ordinarydifferential equations. We show the existence of solutions underthe assumption of weak continuity of the non-linear part. Ifthe non-linear part is monotone decreasing, a solution may beobtained by the QSL method as the strong limit of a quadraticallyconvergent sequence of approximate solutions. Under strongerassumptions on the linear and the non-linear parts, a solutionis quadratically bracketed between two monotone sequences ofapproximate solutions of certain related linear equations. 相似文献
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n阶微分方程三点边值问题 总被引:1,自引:0,他引:1
刘颖 《应用数学与计算数学学报》2001,15(1):29-36
用上、下解方法讨论了非线性n阶常微分方程满足三点全非线性边界条件的边值问题解的存在性和唯一性。 相似文献
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借助上下解方法和锥拉伸与锥压缩不动点定理研究了二阶非线性奇异边值问题u″ λf(t,u(t))=0,0相似文献
12.
This paper investigates the existence of positive solutions of a singular boundary value problem with negative exponent similar
to standard Emden-Fowler equation. A necessary and sufficient condition for the existence of C[0, 1] positive solutions as
well as C1[0, 1] positive solutions is given by means of the method of lower and upper solutions with the Schauder fixed point theorem. 相似文献
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应用锥压缩锥拉伸不动点定理和Leray-Schauder 抉择定理研究了一类具有P-Laplace算子的奇异离散边值问题$$\left\{\begin{array}{l}\Delta[\phi (\Delta x(i-1))]+ q_{1}(i)f_{1}(i,x(i),y(i))=0, ~~~i\in \{1,2,...,T\}\\\Delta[\phi (\Delta y(i-1))]+ q_{2}(i)f_{2}(i,x(i),y(i))=0,\\x(0)=x(T+1)=y(0)=y(T+1)=0,\end{array}\right.$$的单一和多重正解的存在性,其中$\phi(s) = |s|^{p-2}s, ~p>1$,非线性项$f_{k}(i,x,y)(k=1,2)$在$(x,y)=(0,0)$具有奇性. 相似文献
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二阶时滞微分方程边值问题的上下解方法 总被引:1,自引:0,他引:1
主要利用上下解方法和Schauder不动点定理,研究一类二阶时滞微分方程边值问题的正解存在性.为了验证结论的正确性,本文在结尾部分给出了两个例子. 相似文献
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EXISTENCE AND UNIQUENESS FOR SECOND-ORDER VECTOR BOUNDARY VALUE PROBLEM OF NONLINEAR SYSTEMS 总被引:1,自引:0,他引:1
Du Zengji Lin Xiaojie Ge Weigao 《高校应用数学学报(英文版)》2005,20(3):323-330
This paper is concerned with the following second-order vector boundary value problem :x^R=f(t,Sx,x,x'),0〈t〈1,x(0)=A,g(x(1),x'(1))=B,where x,f,g,A and B are n-vectors. Under appropriate assumptions,existence and uniqueness of solutions are obtained by using upper and lower solutions method. 相似文献
18.
本文考虑二阶四点共振边值问题x″(t)=f(t,x(t),x′(t)),0<t<1,x(0)= ax(ξ),x(1)=bx(η).通过建立上下解方法,应用Mawhin重合度理论,获得了一些多解性结果. 相似文献
19.
Xiaojing Yang 《Applied mathematics and computation》2002,130(2-3):225-234
Some sufficient conditions for the existence of positive solutions to Dirichlet boundary value problems of a class of nonlinear second order differential equations are given. 相似文献
20.
将上下解方法和Leray-Shauder度应用到一类含有非线性边界条件的n阶微分方程,得到了至少存在一个解的结果,并且改进和推广了文献中的某些结果. 相似文献