奇异扰动(k, n-k)共轭边值问题的正解

Abstract

Abstract:

In this paper, by employing the so-called modified function, some new existence results of multiple positive solutions for a class of singularly perturbed (k, n-k) conjugate boundary value problems are established, where the perturbed term is only a Lebesgue integrable function. An example is worked out to indicate the application of the main results.

Key words: Conjugate boundary value problems, Singularly perturbed problem, Positive solutions, Modified function, Fixed point index, Cone

CLC Number:

34B15

ZHONG Min-Ling, ZHANG Xin-Guang. Positive Solutions of Singularly Perturbed (k, n-k) Conjugate Boundary Value Problems[J].Acta mathematica scientia,Series A, 2011, 31(1): 263-272.

Trendmd

References

[1] Aris R. Introduction to the Analysis of Chemical Reactors. Englewood Cliffs, NJ: Prentice-Hall, 1965

[2] Castro A, Maya C, Shivaji R. Nonlinear eigenvalue problems with semipositone. Electron J Differ Equ Conf, 2000, 5: 33--49

[3] Anuradha V, Hai D D, Shivaji R. Existence results for superlinear semipositone BVP's. Proc Amer Math Soc, 1996, 124: 757--746

[4] Agarwal R P, O'Regan D. Positive solutions for (p, n-p) conjugate boundary value problems. J Differential Equations, 1998, 150: 462--473

[5] Agarwal R P, Wong F H. Existence of solutions to (k, n-k-2) boundary value problems. Appl Math Comput, 1999, 104: 33--50

[6] Eloe P W, Henderson J. Positive solutions for (n-1, 1) conjugate boundary value problems. Nonlinear Anal, 1997, 28: 1669--1680

[7] Eloe P W, Henderson J. Singular nonlinear (k, n-k) conjugate boundary value problems. J Differential Equations, 1997, 133: 136--151

[8] Guo D J, Lakshmikantham V. Nonlinear Problems in Abstract Cone. New York: Academic Press, Inc, 1988

[9] Kong L J, Wang J Y. The Green's function for (k; n-k) boundary value problems and its application. J Math Anal Appl, 2001, 255: 404--422

[10] Yang X J. Greens function and positive solutions for higher-order ODE. Appl Math Comput, 2003, 136: 379--393

[11] Jiang D Q. Positive solutions to singular (k, n-k) conjugate boundary value problems. Acta Math Sinica, 2001, 3: 541--548

[12] Loud W. Periodic solutions of a perturbed autonomous system. Ann of Math, 1959, 70: 490--529

[13] Xia Y, Huang Z, Han M. Existence of almost periodic solutions for forced perturbed systems with piecewise constant argument. J Math Anal Appl, 2007, 333: 798--816

[14] Khanmamedov A. On the existence of a global attractor for the wave equation with nonlinear strong damping perturbed by nonmonotone term. Nonlinear Anal, 2008, 69: 3372--3385

[15] Llibre J, Wu H, Yu J. Linear estimate for the number of limit cycles of a perturbed cubic polynomial differential system. Nonlinear Anal, 2009, 70: 419--432

[16] Makarenkov O, Nistri P. Periodic solutions for planar autonomous systems with nonsmooth periodic perturbations. J Math Anal Appl, 2008, 338: 1401--1417

[17] Cen Z. A second-order difference scheme for a parameterized singular perturbation problem. J Comput Appl Math, 2008, 221: 174--182

Positive Solutions of Singularly Perturbed (k, n-k) Conjugate Boundary Value Problems

PDF (PC)

Abstract

Cite this article

share this article

References

Related Articles 15

Metrics

Comments

Recommended 10

[1]	Wang Jianyong. The Theorems of Embedding Normed Cones into Normed Linear Spaces and the Hahn-Banach Extension Theorems [J]. Acta mathematica scientia,Series A, 2017, 37(6): 1040-1052.
[2]	Li Haixia. Stability and Uniqueness of Positive Solutions for a Food-Chain Model [J]. Acta mathematica scientia,Series A, 2017, 37(6): 1094-1104.
[3]	Liao Jiafeng, Li Hongying. Existence and Multiplicity of Positive Solutions for the Superlinear Kirchhoff-Type Equations with Critical Sobolev Exponent [J]. Acta mathematica scientia,Series A, 2017, 37(6): 1119-1124.
[4]	Wang Shengjun, Han Yazhou. Generalized Picone's Identity and Its Applications for Heisenberg-Greiner Operators [J]. Acta mathematica scientia,Series A, 2017, 37(5): 895-901.
[5]	Hao Xinan, Liu Lishan. Positive Solutions for Nonlocal Boundary Value Problems of Fourth Order Differential Equation with Parameters [J]. Acta mathematica scientia,Series A, 2017, 37(2): 287-298.
[6]	Dong Xiaoyu, Bai Zhanbing, Sun Sujing. Positive Solutions for Some Boundary Value Problems with Conformable Fractional Differential Derivatives [J]. Acta mathematica scientia,Series A, 2017, 37(1): 82-91.
[7]	Long Pinhong, Han Huili, Deng Guantie. Covering Properties for Rarefied Sets Associated with the Stationary Schrödinger Operator at Infinity in a Cone [J]. Acta mathematica scientia,Series A, 2016, 36(6): 1082-1091.
[8]	He Zerong, Yang Lizhi. A Weighted Population Model with Size-Structure: Stability and Optimal Harvesting [J]. Acta mathematica scientia,Series A, 2016, 36(3): 584-600.
[9]	Huang Zhenggang. A New Notion of Generalized Subgradients and Its Properties [J]. Acta mathematica scientia,Series A, 2015, 35(5): 927-935.
[10]	Zhang Yunsheng, Gao Leifu. A Smoothing Inexact Newton Method for Symmetric Cone Complementarity Problems [J]. Acta mathematica scientia,Series A, 2015, 35(4): 824-832.
[11]	Huang Huaping, Xu Shaoyuan, Xu Wangbin. T-Stability of Picard's Iteration in Cone Metric Spaces [J]. Acta mathematica scientia,Series A, 2015, 35(2): 395-404.
[12]	PIAO Yong-Jie, JIN Hai-Lan, JIN Yuan-Feng. Unique Common Fixed Points for Four Mappings on \|TVS-Valued Cone Metric Spaces [J]. Acta mathematica scientia,Series A, 2015, 35(1): 172-181.
[13]	LI Bo, LIU Han. Positive Solutions of the Predator-Prey Model with Diffusion and Cross Diffusion [J]. Acta mathematica scientia,Series A, 2014, 34(6): 1578-1586.
[14]	ZHANG Wen-Li, ZHONG Li-Nan. Multiplicity of Positive Solutions for a (p, q-Laplacian Elliptic Systems in R^N [J]. Acta mathematica scientia,Series A, 2014, 34(5): 1264-1274.
[15]	HE Ze-Rong, LIU Rong, LIU Li-Li. Optimal Harvest Rate for a Population System Modeling Periodic Environment and Body Size [J]. Acta mathematica scientia,Series A, 2014, 34(3): 684-690.