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1.
田颖辉 《大学数学》2017,33(3):14-19
基于格林函数理论,主要利用Lerray-Schauder抉择定理和上下解方法针对半正定条件下,奇异超线性二阶周期边值问题正解的存在性进行推理证明,获取了奇异超线性二阶周期边值问题的一个正解.  相似文献   

2.
应用锥中的不动点定理研究奇异二阶三点边值问题的正解的存在性。采用一种构造Green函数的方法为出发点,利用分段定义算子的手法讨论更一般的奇异二阶三点边值问题。得到了一个正解的存在性定理。其中的非线性项可以是变号的。  相似文献   

3.
该文利用锥不动点定理讨论了奇异半正二阶脉冲Dirichlet边值问题正解的存在性.  相似文献   

4.
姚庆六 《数学学报》2012,(5):903-918
改进了奇异非线性边值问题的经典Agarwal-O'Regan方法.利用这个改进的方法建立了奇异非线性(p,n-p)共轭边值问题正解的局部存在性与多解性,其中允许非线性项关于时间和空间变元同时奇异.主要工具是锥拉伸与锥压缩型的Guo-Krasnosel'skii不动点定理和精确先验估计技巧.特别的,考察了非自治奇异非线性二阶、三阶、四阶共轭边值问题.  相似文献   

5.
讨论一类奇异二阶微分方程的边值问题,给出了正解存在和不存在的准则。  相似文献   

6.
奇异二阶泛函微分方程边值问题的多重正解   总被引:9,自引:2,他引:7  
本文把ZhaoliLiu和Erbe等人关于常微分方程边值问题多重正解的工作推广到二阶奇异混合型泛函微分方程边值问题,证明了所考虑的方程边值问题存在至少两个正解的充分条件。  相似文献   

7.
奇异边值问题的边界非正则正解   总被引:1,自引:0,他引:1  
刘希玉 《应用数学》1998,11(2):32-40
本文讨论一类二阶奇异边值问题正解的存在性.证明了这类问题存在边界非正则正解.  相似文献   

8.
利用不动点指数理论研究奇异二阶周期边值问题.在有关其线性算子方程对应的第一特征值的条件下得到边值问题正解的存在性,推广和改进了最近文献的结果.  相似文献   

9.
二阶奇异边值问题的正解   总被引:6,自引:0,他引:6       下载免费PDF全文
利用Leary-Schauder不动点定理讨论了一类二阶奇异边值问题正解的存在性问题,并给出了一个正解存在的必要条件  相似文献   

10.
二阶奇异微分方程组边值问题两个正解的存在性   总被引:1,自引:0,他引:1  
利用锥拉伸和锥压缩不动点定理,给出了一类二阶微分方程组奇异边值问题两个正解的存在性.  相似文献   

11.
We consider boundary value problems of arbitrary order for linear differential equations on a geometric graph. Solutions of boundary value problems are coordinated at the interior vertices of the graph and satisfy given conditions at the boundary vertices. For considered boundary value problems, we construct adjoint boundary value problems and obtain a self-adjointness criterion. We describe the structure of the solution set of homogeneous self-adjoint boundary value problems with alternating coefficients of a differential equation and obtain nondegeneracy conditions for these boundary value problems.  相似文献   

12.
In this article we present a new fixed point theorem for a class of general mixed monotone operators, which extends the existing corresponding results. Moreover, we establish some pleasant properties of nonlinear eigenvalue problems for mixed monotone operators. Based on them the local existence-uniqueness of positive solutions for nonlinear boundary value problems which include Neumann boundary value problems, three-point boundary value problems and elliptic boundary value problems for Lane-Emden-Fowler equations is proved. The theorems for nonlinear boundary value problems obtained here are very general.  相似文献   

13.
一类Dirichlet边值逆问题   总被引:2,自引:0,他引:2  
给出解析函数的一类Dirichlet边值逆问题的数学提法.依据解析函数Dirichlet边值问题和广义Dirichlet边值问题的理论,讨论了此边值逆问题的可解性.利用解析函数Dirichlet边值问题的Schwarz公式,给出了该边值逆问题的可解条件和解的表示式.  相似文献   

14.
We suggest a new approach to the statement of boundary value problems for elliptic partial differential equations on arbitrary Riemannian manifolds which is based on the consideration of equivalence classes of functions on a manifold. Using this approach, we establish some interrelation between the solvability of boundary value problems and solvability of exterior boundary problems for the stationary Schrodinger equation. Also we prove the comparison and uniqueness theorems for solutions to boundary value problems in this statement and obtain sufficient conditions for solvability of boundary value problems when the coefficient in the Schrodinger equation is changed.  相似文献   

15.
We investigate general Shapiro-Lopatinsky elliptic boundary value problems on manifolds with polycylindrical ends. This is accomplished by compactifying such a manifold to a manifold with corners of in general higher codimension, and we then deal with boundary value problems for cusp differential operators. We introduce an adapted Boutet de Monvel's calculus of pseudodifferential boundary value problems, and construct parametrices for elliptic cusp operators within this calculus. Fredholm solvability and elliptic regularity up to the boundary and up to infinity for boundary value problems on manifolds with polycylindrical ends follows.  相似文献   

16.
一类广义解析函数的Riemann边值逆问题   总被引:8,自引:0,他引:8  
温小琴  李明忠 《数学杂志》2004,24(4):457-464
本文给出了一类有关广义解析函数Riemann边值逆问题的数学提法.在将此边值逆问题转化为边值问题的基础上,借助于广义解析函数边值问题的相关理论,分别获得了此边值逆问题在正则型和非正则型情况下的解.  相似文献   

17.
We study subsolutions for semilinear elliptic boundary value problems in L1. We consider as well nonlinear as linear boundary conditions. The nonlinear functions may be multivated. We characterize in terms of p.d.e. the subsolutions defined by a nonlinear functional analysis argument. Applications are given to obtain existence results for semilinear elliptic boundary value problems and comparison and estimates for nonlinear parabolic boundary value problems.  相似文献   

18.
We consider boundary value problems for an elastic medium bounded by a cylindrical surface on which a load with a constant-in-time form is moving at a constant subsonic velocity. This class of problems is a model class for the dynamics of underground structures like transport tunnels and ground transport. The method of generalized functions is developed for the solution of boundary value problems. We construct dynamic analogs of Green formulas and use them to derive singular boundary integral equations, which solve the considered boundary value problems.  相似文献   

19.
This paper investigates the analytical approximate solutions of third order three-point boundary value problems using reproducing kernel method. The solution obtained by using the method takes the form of a convergent series with easily computable components. However, the reproducing kernel method can not be used directly to solve third order three-point boundary value problems, since there is no method of obtaining reproducing kernel satisfying three-point boundary conditions. This paper presents a method for solving reproducing kernel satisfying three-point boundary conditions so that reproducing kernel method can be used to solve third order three-point boundary value problems. Results of numerical examples demonstrate that the method is quite accurate and efficient for singular second order three-point boundary value problems.  相似文献   

20.
In this paper we consider the effect of concave nonlinearities for the solution structure of nonlinear boundary value problems such as Dirichlet and Neumann boundary value problems of elliptic equations and periodic boundary value problems for Hamiltonian systems and nonlinear wave equations.  相似文献   

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