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1.
一类四阶次线性奇异边值问题的正解   总被引:9,自引:0,他引:9  
韦忠礼 《数学学报》2005,48(4):727-738
本文利用极大值原理和通过构造上下解给出了一类四阶次线性微分方程的奇异边值问题有C2[0,1]和C3[0,1]正解存在的充分必要条件.  相似文献   

2.
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   

3.
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   

4.
负指数EmdenFowler方程奇异边值问题的正解   总被引:9,自引:2,他引:9  
本文利用上下解方法和不动点理论给出了负指数EmdenFowler方程奇异边值问题有C[0,1]和C1[0,1]正解存在的充分必要条件.  相似文献   

5.
负指数Emden Fowler方程奇异边值问题的正解   总被引:27,自引:3,他引:27  
韦忠礼 《数学学报》1998,41(3):655-662
本文利用上下解方法和不动点理论给出了负指数Emden Fowler方程奇异边值问题有C[0,1]和C1[0,1]正解存在的充分必要条件.  相似文献   

6.
奇异四阶积分边值问题正解的存在唯一性   总被引:1,自引:0,他引:1  
利用上下解方法结合极值原理研究了具有积分边值条件的奇异四阶微分方程正解的存在、唯-性,给出了C~2[0,1]和C~3[0,1]正解存在唯一的充分条件.非线性项f(t,χ)允许在t=0,1和χ=0处具有奇异性.  相似文献   

7.
一类高阶奇异边值问题的正解   总被引:5,自引:1,他引:4  
杨小京 《数学学报》2002,45(2):379-382
本文利用上下解方法给出一类高阶微分方程的奇异边值问题正解的充分条件,改进并推广了韦忠礼在文献[1]中的结果,并指出其证明的漏洞.  相似文献   

8.
张兴秋 《系统科学与数学》2010,10(10):1407-1416
利用上下解方法结合极值原理研究一类带积分边值条件的奇异二阶微分方程正解的存在性以及唯一性,给出了$C[0,1]$和$C^1[0,1]$正解存在唯一的一个充分条件.非线性项允许在$t=0,1$ 和$x=0$处具有奇异性.  相似文献   

9.
四阶奇异边值问题的正解   总被引:56,自引:0,他引:56  
韦忠礼 《数学学报》1999,42(4):715-722
本文利用上下解方法和极大值原理给出了四阶微分方程的奇异边值问题有C2[0,1]和C3[0,1]正解存在的充分必要条件.  相似文献   

10.
边界条件含参数的二阶奇异非线性边值问题   总被引:1,自引:0,他引:1  
利用不动点指数理论以及上下解方法得到了边界条件含参数的二阶奇异非线性边值问题的正解存在性结果,该结果推广了已有文献中的众多结果.  相似文献   

11.
Some properties of minimal solutions for a fuzzy relation equation   总被引:7,自引:0,他引:7  
Some properties of the solution set and minimal solutions of a fuzzy relation equation are considered. In this paper, we show the necessary and sufficient condition for existence of a minimal solution of a finite fuzzy relation equation defined on infinite index sets.  相似文献   

12.
In this paper, a class ofN-person, nonzero-sum differential games with state-dependent closed-loop feedback solutions is presented. In particular, the system of Hamilton-Jacobi equations for a closed-loop feedback solution turns out to be a set ofN-independent linear equations with viscosity solutions.The helpful comments of an anonymous referee are gratefully acknowledged.  相似文献   

13.
In this paper, we characterize the nonemptiness and compactness of the set of weakly efficient solutions of a convex vector optimization problem with cone constraints in terms of the level-boundedness of the component functions of the objective on the perturbed sets of the original constraint set. This characterization is then applied to carry out the asymptotic analysis of a class of penalization methods. More specifically, under the assumption of nonemptiness and compactness of the weakly efficient solution set, we prove the existence of a path of weakly efficient solutions to the penalty problem and its convergence to a weakly efficient solution of the original problem. Furthermore, for any efficient point of the original problem, there exists a path of efficient solutions to the penalty problem whose function values (with respect to the objective function of the original problem) converge to this efficient point.  相似文献   

14.
This paper is concerned with finding two solutions of a set covering problem that have a minimum number of variables in common. We show that this problem is NP-complete, even in the case where we are only interested in completely disjoint solutions. We describe three heuristic methods based on the standard greedy algorithm for set covering problems. Two of these algorithms find the solutions sequentially, while the third finds them simultaneously. A local search method for reducing the overlap of the two given solutions is then described. This method involves the solution of a reduced set covering problem. Finally, extensive computational tests are given demonstrating the nature of these algorithms. These tests are carried out both on randomly generated problems and on problems found in the literature.  相似文献   

15.
A general framework is presented in which the relation of the set of noninferior points and the set of compromise solutions is studied. It is shown that the set of compromise solutions is dense in the set of noninferior points and that each compromise solution is properly noninferior. Also, under convexity of the criteria space, a characterization of the properly noninferior points in terms of the compromise solutions is presented. In this characterization, the compromise solutions depend continuously on the weights. Use of the maximum norm is studied also. It is shown that a subset of these max-norm solutions, obtained by taking certain limits of compromise solutions, is dense and contained in the closure of the set of noninferior points.  相似文献   

16.
The concepts of domination structures and nondominated solutions are important in tackling multicriteria decision problems. We relax Yu's requirement that the domination structure at each point of the criteria space be a convex cone (Ref. 1) and give results concerning the set of nondominated solutions for the case where the domination structure at each point is a convex set. A practical necessity for such a generalization is discussed. We also present conditions under which a locally nondominated solution is also a globally nondominated solution.  相似文献   

17.
The paper deals with an initial boundary-value problem for a parabolic inclusion whose multivalued term has the structure of a difference between the Clarke generalized gradient of some locally Lipschitz function verifying a unilateral growth condition and the subdifferential of a convex function, and where the elliptic part is expressed by a general quasilinear operator of the Leray-Lions type. Our results address not only the existence of solutions, but also the extremality inside an order interval determined by appropriately defined upper and lower solutions as well as the compactness of the solution set in suitable spaces.  相似文献   

18.
In this paper, the laminar film condensation of saturated stream on an isothermal vertical plate is studied. The boundary layer equations of momentum and thermal energy are reduced to two ordinary differential equations by means of a set of similarity transformations. The problem is then solved analytically using the homotopy analysis method (HAM). The dual solutions are obtained for a range of values of the parameter ηδ. However, it should be noted that the second branch solution of the considered problem has only mathematical meanings. The present work shows the validity and the great potentiality of the proposed technique for the nonlinear problems with multiple solutions.  相似文献   

19.
In the classical level set method, the slope of solutions can be very small or large, and it can make it difficult to get the precise level set numerically. In this paper, we introduce an improved level set equation whose solutions are close to the signed distance function to evolving interfaces. The improved equation is derived via approximation of the evolution equation for the distance function. Applying the comparison principle, we give an upper- and lower bound near the zero level set for the viscosity solution to the initial value problem.  相似文献   

20.
结合齐次平衡法原理并利用(G'/G)-展开法,研究了广义的(2+1)维ZK-MEW方程的精确解,从而得到了广义的(2+1)维ZK-MEW方程的用双曲函数和三角函数表示的通解,当双曲函数通解中常数取特殊值时,便得到广义的(2+1)维ZK-MEW方程的孤立波解,获得了与现有文献不同的新精确解.  相似文献   

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