一类半正非线性多点边值问题多个正解的存在性

Abstract

Abstract:

Under some suitable local conditions and superlinear or sublinear conditions, we establish the multiplicity of positive solutions for a class of singular semipositone multi-point boundary value problem. Our results extend and improve some existing results of previous literatures for two-point and multi-point boundary value problems in the positone and in the semipositone cases.

Key words: Singular boundary value problems, Semipositone, Positive solutions, Fixed point, Cone

CLC Number:

34B15

ZHANG Xin-Guang, PAN Chuan-Zhong. Exsitence of Multiple Positive Solutions for a Semipositone Nonlinear Multi-point Boundary Value Problems[J].Acta mathematica scientia,Series A, 2012, 32(5): 996-1010.

Trendmd

References

[1] Il'in V, Moiseev E. Nonlocal boundary value problem of the second kind for Sturm-Liouville operator. Diff Eqs, 1987, 23: 803--810

[2] Gupta C. Solvability of a three-point nonlinear boundary value problem for a second order ordinary differential equation. J Math Anal Appl, 1992, 168: 540--551

[3] Erbe H, Hu S, Wang H. Multiple positive solutions of some boundary value problems. J Math Anal Appl, 1994, 203: 640--648

[4] Ma R. Multiple positive solutions for nonlinear m-point boundary value problems. Appl Math Comput, 2004, 148: 249--262

[5] Ma R,  Thompson B. Positive solutions for nonlinear m-point boundary eigenvalue problems. J Math Anal Appl, 2004, 297: 24--37

[6] Zhang X, Liu L. Positive solutions of fourth-order multi-point boundary value problems with bending term.  Appl Math Comput, 2007, 194: 321--332

[7] Feng M,   Xie D. Multiple positive solutions of multi-point boundary value problem for second-order impulsive differential equations. J Compu Appl Math, 2009, 223: 438--448

[8] Liu B. Positive solutions of a nonlinear three-point boundary value problem. Appl Math Comput, 2002, 132: 11--28

[9] Pang H, Ge W. Existence results for some fourth-order multi-point boundary value problem. Mathematical and Computer Modelling, 2009, 49: 1319--1325

[10] Graef J, Kong L. Necessary and sufficient conditions for the existence of symmetric positive solutions of multi-point boundary value problems. Nonlinear Anal, 2008, 68: 1529--1552

[11] Zhang X, Zou H, Liu L. Positive solutions of second-order m-point boundary value problems with changing sign singular nonlinearity. Applied Mathematics Letters, 2007, 20: 629--636

[12] Ma R. Existence of positive solutions for superlinear semipositone m-point boundary-value problems. Proc Edinburgh Math Soc, 2003, 46: 279--292

[13] Lan K. Multiple positive solutions of semi-positone Sturm-Liouville boundary value problems. Bull London Math Soc, 2006, 38: 283--293

[14] Lan K. Positive solutions of semi-positone Hammerstein integral equations and applications. Commun Pure Appl Anal, 2007, 6: 441--451

[15] Xu X, O'Regan D. Existence of positive solutions for operator equations and applications to semipositone problems. Positivity, 2006, 10: 315--328

[16] Zhang X. Existence of positive solution to superlinear semipositone singular m-point boundary value problems. Ann Differential Equations, 2008, 24: 490--497

[17] Dong S, Zhou H. Two positive solutions of M-point boundary value problems with sign changing nonlinearities. Nonlinear Funct Anal Appl, 2005, 10: 89--102

[18] Dong S, Ge W. Positive solutions of an m-point boundary value problem with sign changing nonlinearities. Comput Math Appl, 2005, 49: 589--598

[19] Ma Q. Positive solutions of sublinear semipositone multi-point boundary value problem. J Lanzhou Univ Nat Sci, 2003, 39: 5--7

[20] Webb J, Infante G. Semi-positone nonlocal boundary value problems of arbitrary order. Commun Pure Appl Anal, 2010, 9: 563--581

[21] Yao Q. Existence and multiplicity of positive solutions to a semipositone (N, P) boundary value problem. Indian J Pure Appl Math, 2009, 40: 3--19

[22] Yang C. Multiple positive solutions for semipositone m-point boundary value problems. Gongcheng Shuxue Xuebao, 2009, 26: 349--356

[23] Yang L, Shen C, Liu X, Jia M. Positive solutions for a second-order multi-point boundary value problem with sign-changing nonlinearity. J Systems Sci Math Sci (in Chinese), 2009, 29: 980--988

[24] Zhang Q, Jiang D. Multiple solutions to semipositone Dirichlet boundary value problems with singular dependent nonlinearities for second order three-point differential equations. Comput Math Appl, 2010, 59: 2516--2527

[25] Guo D, Lakshmikantham V. Nonlinear Problems in Abstract Cones. New York: Academic Press, 1988

Exsitence of Multiple Positive Solutions for a Semipositone Nonlinear Multi-point Boundary Value Problems

PDF (PC)

Abstract

Cite this article

share this article

References

Related Articles 15

Metrics

Comments

Recommended 10

[1]	Piao Yongjie. Improvements of Fixed Point Theorems for Mappings with AContractions on Metric Spaces [J]. Acta mathematica scientia,Series A, 2018, 38(5): 855-863.
[2]	Zou Xia, Wu Shiliang. Traveling Waves in a Nonlocal Dispersal SIR Epidemic Model with Delay and Nonlinear Incidence [J]. Acta mathematica scientia,Series A, 2018, 38(3): 496-513.
[3]	Chang Shih-sen, Liu Zhenhai, Wen Ching-Feng, Tang Jinfang. Split Variational Inclusion Problem Involving Fixed Point for an Asymptotically Nonexpansive Semigroup with Application to Optimization Problem [J]. Acta mathematica scientia,Series A, 2018, 38(2): 231-243.
[4]	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.
[5]	Li Haixia. Stability and Uniqueness of Positive Solutions for a Food-Chain Model [J]. Acta mathematica scientia,Series A, 2017, 37(6): 1094-1104.
[6]	Guo Tingguang, Xu Zhiting. Existence of Traveling Waves in a Spatial Infectious Disease Model with Vaccination [J]. Acta mathematica scientia,Series A, 2017, 37(6): 1129-1147.
[7]	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.
[8]	Song Jiping, Wang Maofa. Common Fixed Point Results for Generalized Weak Contractions with a Rational Expression in Ordered Partial Metric Spaces [J]. Acta mathematica scientia,Series A, 2017, 37(3): 401-415.
[9]	Wang Xuewu. Convergence and Stability of Ishikawa Type Iterative Sequences for the φ-Hemi Pseudocontractive Operator Pair [J]. Acta mathematica scientia,Series A, 2017, 37(2): 248-256.
[10]	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.
[11]	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.
[12]	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.
[13]	Cai Gang, Yekini Shehu. Viscosity Iterative Algorithm for Variational Inequality Problems and Fixed Point Problems of Strict Pseudo-Contractions in q-Uniformly Smooth and Uniformly Convex Banach Spaces [J]. Acta mathematica scientia,Series A, 2016, 36(4): 623-638.
[14]	Deng Weiqi. A System of Split Equilibrium Problems for Sequences of Bifunctions [J]. Acta mathematica scientia,Series A, 2016, 36(4): 763-770.
[15]	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.