共查询到19条相似文献,搜索用时 140 毫秒
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变分方法与反向上下解 总被引:4,自引:1,他引:3
本文在非线性方程的下解不小于上解这一条件(即反向上下解条件)下研究了其解的存在性.我们证明了,如果非线性算子方程有变分结构,有一对反向上下解,对应的算子映某个锥入锥并且满足一定的辅助条件,那么这一方程在锥中至少有两个解.另外,本文还研究了反向上下解条件下非线性椭圆边值问题正解的存在性. 相似文献
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本文用Schauder不动点定理证明了一类用上下解方法难以解决的脉冲微分方程边值问题解的存在性,改进现有的一些结果。 相似文献
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代丽美 《应用泛函分析学报》2007,9(1):40-55
利用不动点定理得到了脉冲奇异混合边值问题的上下解方法,并且利用此方法得到了负指数的脉冲Emden—Fowler方程奇异混合边值问题正解存在的充分必要条件. 相似文献
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带有"上确界"的非线性脉冲微分方程无穷边值问题 总被引:1,自引:0,他引:1
戚仕硕 《应用泛函分析学报》2004,6(3):200-208
应用上下解方法和单调迭代技术研究了带有上确界的一阶非线性脉冲微分方程无穷边值问题,并获得了其极值解的存在性结果. 相似文献
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In this paper, we first give the method of lower and upper solutions for the existence of positive solutions to a singular impulsive boundary value problem. Then we obtain a necessary and sufficient condition for the existence of positive solutions of Emden–Fowler singular impulsive boundary value problem by means of the method of lower and upper solutions. 相似文献
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Lixin Zhang Bo Sun Chunfeng Xing .Dept.of Basic Courses Beijing Union University Beijing ;. 《Annals of Differential Equations》2012,(3):368-372
In this paper,we study the existence of solutions to a third-order three-point boundary value problem.By imposing certain restrictions on the nonlinear term,we prove the existence of at least one solution to the boundary value problem by the method of lower and upper solutions.We are interested in the construction of lower and upper solutions. 相似文献
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代丽美 《应用泛函分析学报》2007,9(1):40-55
利用不动点定理得到了脉冲奇异混合边值问题的上下解方法,并且利用此方法得到了负指数的脉冲Emden-Fowler方程奇异混合边值问题正解存在的充分必要条件. 相似文献
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On fourth-order elliptic boundary value problems 总被引:4,自引:0,他引:4
C. V. Pao 《Proceedings of the American Mathematical Society》2000,128(4):1023-1030
This paper is concerned with the existence and uniqueness of a solution for a class of fourth-order elliptic boundary value problems. The existence of a solution is proven by the method of upper and lower solutions without any monotone nondecreasing or nonincreasing property of the nonlinear function. Sufficient conditions for the uniqueness of a solution and some techniques for the construction of upper and lower solutions are given. All the existence and uniqueness results are directly applicable to fourth-order two-point boundary value problems.
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Fengjie Geng Yancong Xu Deming Zhu 《Nonlinear Analysis: Theory, Methods & Applications》2008,69(11):4074-4087
This paper deals with the periodic boundary value problem for a class of first-order impulsive dynamic equations on time scales. We introduce a new notion of lower and upper solutions, which extends the classical lower and upper solutions. The existence of extremal solutions is presented by virtue of the method of lower and upper solutions coupled with monotone iterative technique. An example is also included to illustrate the main results. 相似文献
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研究了含p-Laplacian算子的奇异四阶四点边值问题,利用上下解方法与Schauder不动点定理,获得了至少一个C~3[0,1]正解的存在性结果. 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