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 共查询到19条相似文献,搜索用时 78 毫秒
1.
Banach空间半线性发展方程的周期解   总被引:8,自引:2,他引:8  
李永祥 《数学学报》1998,41(3):629-636
把上、下解方法引入到有序Banach空间中的半线性发展方程周期解问题,利用正算子半群特征与单调迭代程序,获得了最大周期解与最小周期解的存在性.所得的结果概括和推广了常微分方程与偏微分方程中的有关结论  相似文献   

2.
Banach空间常微分方程理论的若干问题   总被引:3,自引:0,他引:3  
郭大钧  孙经先 《数学进展》1994,23(6):492-504
本文综述了Banach空间常微分方程理论近期的发展,主要为紧型条件,耗散型条件,非线性半群、上下解方法,边值问题、Banach空间中的积-微分方程和脉冲方程,以及对于不动点理论和临界理论的应用,并且给出了作者们在这一领域中的一些新结果。  相似文献   

3.
利用一个新的比较结果和Monech不动点定理证明了Banach空间中非线性脉冲Volterra型积分方程整体解的存在性定理,并给出了对Banach空间中一阶脉冲微分方程初值问题的应用,改进了文(1-3)中的主要结果。  相似文献   

4.
Banach空间中超线性Hammerstein型积分方程的解及其应用   总被引:2,自引:0,他引:2  
娄本东 《数学学报》1996,39(6):756-763
本文利用不动点指数理论研究Banach空间中超线性Hammerstein型积分方程正解及非零解的存在性,并应用于Banach空间中超线性常微分方程的Sturm-Liouville问题,最后,本文给出了一个非线性常微分方程无穷组存在正解的例子.  相似文献   

5.
非线性算子方程迭代解的存在性定理及其应用   总被引:8,自引:1,他引:7       下载免费PDF全文
在Banach空间中,利用锥理论和单调迭代方法研究了一类非线性算子方程的解和最小最大耦合解的存在与迭代逼近定理,并应用到Banach空间中非线性Volterra型积分方程和常微分方程的初值问题.  相似文献   

6.
Banach空间中两点边值问题解的存在唯一性   总被引:7,自引:0,他引:7  
利用半序方法,得到Banach空间中二阶常微分方程两点边值问题解的存在唯一性定理.  相似文献   

7.
本文利用不动定理研究Banach空间中一类非线性积分微分方程解的存在性,推广了一些已知结果。  相似文献   

8.
Banach空间中一类非线性积分微分方程解的存在性   总被引:2,自引:1,他引:1  
本文利用不动点定理研究Banach空间中一类非线性积分微分方程解的存在性,推广了一些已知结果。  相似文献   

9.
郭玉霞 《应用数学》1998,11(4):38-42
借助于锥理论,本文讨论Banach空间中非线性脉冲积分微分方程的解,给出一阶脉冲微分方程存在唯一正解的条件及混合型脉冲积分微分方程至少具有两解的条件。  相似文献   

10.
本文研究Banach空间中常微分方程的周期解的存在性,在耗散型条件下得到一系列结果。同时,还给出一无穷维微分方程存在周期解的例子。  相似文献   

11.
This paper investigates the existence and multiplicity of positive solutions for a class of nonlinear boundary-value problem of second-order differential equations with integral boundary conditions in ordered Banach spaces. The arguments are based upon a specially constructed cone and the fixed point theory in a cone for strict set contraction operators. The nonexistence of a positive solution is also studied.  相似文献   

12.
Chen  Yong-Zhuo 《Positivity》2002,6(1):47-57
This paper considers the stability of positive fixed points of nonlinear operators under purturbations. Through the use of the Thompson's metric, we obtain the results in ordered Banach spaces by proving the corresponding results in metric spaces first. An application to the existence of periodic solutions for a parametrized system of ordinary differential equations is given.  相似文献   

13.
This paper investigates the multiplicity of positive solutions for a class of nonlinear boundary-value problems of fourth-order differential equations with integral boundary conditions in ordered Banach spaces. The arguments are based upon a specially constructed cone and the fixed point index theory in cone for strict set contraction operator. The nonexistence of positive solution is also studied. Meanwhile, an example is worked out to demonstrate the main results.  相似文献   

14.
In this paper, we prove existence, uniqueness and comparison results for solutions of differential and integral equations in Banach spaces containing Henstock–Kurzweil integrable functions from a compact real interval to an ordered Banach space.  相似文献   

15.
讨论了有序Banach空间E中的非线性常微分方程:u′(t)+Mu(t)=f(t,u(t)),(?)t∈R正ω-周期解的存在性,其中f:R×P→P连续,P为E中的正元锥.通过新的非紧性测度的估计技巧与凝聚映射的不动点指数理论获得了该问题正ω-周期解的存在性结果.  相似文献   

16.
研究了半序Banach空间中一类非线性锥映射歧点的存在性与正特征元的全局结构.与已知文献不同的是,不要求算子在零点沿着锥Frechet可微. 作为应用,讨论了一类椭圆型偏微分方程边值问题正解的歧点与全局结构.  相似文献   

17.
This paper investigates the existence, nonexistence, and multiplicity of positive solutions for a class of nonlinear boundary-value problems of third order differential equations with integral boundary conditions in ordered Banach spaces by means of fixed-point principle in cone and the fixed-point index theory for strict set contraction operator. In addition, an example is worked out to demonstrate the main results.  相似文献   

18.
In this paper, we study the existence and uniqueness of positive solutions for a class of nonlinear operator equations on ordered Banach spaces. Various applications are also considered to illustrate our obtained results (existence of solutions to quadratic integral equations with a linear modification of the argument, positive solution of second-order Neumann boundary value problem, and positive definite solutions of a class of nonlinear matrix equations).  相似文献   

19.
In this paper, we study a class of nonlinear operator equations with more extensive conditions in ordered Banach spaces. By using the cone theory and Banach contraction mapping principle, the existence and uniqueness of solutions for such equations are investigated without demanding the existence of upper and lower solutions and compactness and continuity conditions. The results in this paper are applied to a class of abstract semilinear evolution equations with noncompact semigroup in Banach spaces and the initial value problems for nonlinear second-order integro-differential equations of mixed type in Banach spaces. The results obtained here improve and generalize many known results.  相似文献   

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