JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2016, Vol. 51 ›› Issue (6): 42-48.doi: 10.6040/j.issn.1671-9352.0.2015.434

Previous Articles     Next Articles

Existence of multiple of solutions of first order multi-point boundary value problem

ZHU Wen-wen   

  1. College of Mathematics and Statistics, Northwest Normal University, Lanzhou 730070, Gansu, China
  • Received:2015-09-14 Online:2016-06-20 Published:2016-06-15

PDF (PC)

723

Abstract: We use the method of the upper and lower solutions and topological degree theory to study existence of multiple solutions of first order differential equations multi-point boundary value problem{u'(t)=f(t,u(t)), t∈［0,T］,u(0)+∑mk=1aku(tk)=cwhere c∈R, tk(k=1,2,3,…,m)satisfy 012<…mk<0 are constants, and 1+∑mk=1ak>0, f∈C(［0,T］×R, R). Finally, an example is presented to illustrate the application of the obtained result.

Key words: topological degree theory, multi-point boundary value problem, upper and lower solutions

CLC Number: 

  • O175.8
[1] MOSHINSKY M. Sobre los problemas de condiciones a la frontiera en una dimension de caracteristicas discontinuas[J]. Boletín de la Sociedad Matemática Mexicana, 1950, 7:1-25.
[2] TIMOSHENKO S P, GERE J M. Theory of elastic stability[J]. New York: McGrawHill, 1961.
[3] ILIN V A, MOISEEV E I. Nonlocal boundary value problem of the second kind for a Sturm-Liouville operator[J]. Differential Equations, 1987, 23(8):979-987.
[4] GUPTA C P, TROFIMCHUK S I. A sharper condition for the solvability of a three-point second order boundary value problem[J]. Journal of Mathematical Analysis and Applications, 1997, 205(2):586-597.
[5] MA Ruyun. Positive solutions of a nonlinear three-point boundary valueproblem[J]. Electronic Journal of Differential Equations, 1999, 34:1-8.
[6] KONG Lingju, KONG Qingkai. Uniqueness and parameter dependence of solutions of second-order boundary value problems[J]. Applied Mathematics Letters, 2009, 22(11):1633-1638.
[7] REUTSKIY S Y. A method of particular solutions for multi-point boundary value problems[J]. Applied Mathemaatics and Computation, 2014, 243:559-569.
[8] KONG Lingju, WONG J S W. Positive solutions for higher order multi-point boundary value problems with nonhomogeneous boundary conditions[J]. Journal of Mathematical Analysis and Applications, 2010, 367(2):588-611.
[9] JIANG Weihua, WANG Bin. Positive solutions for second-order multi-point boundary-value problems at resonance in Banach spaces[J]. Electronic Journal of Differential Equations, 2011, 22:1-11.
[10] SUN Wen, CHEN Shihua, ZHANG Qunqiao, WANG Changping. Existence of positive solutions to n-point nonhomogeneous boundary value problems[J]. Journal of Mathematical Analysis and Applications, 2007, 330(1):612-621.
[11] 马如云. 非线性常微分方程非局部问题[M]. 北京: 科学出版社, 2004:23-27. MA Ruyun. Nonlocal problems of nonlinear ordinary differential equations[M]. Beijing: Science Press, 2004:23-27.
[12] MA Ruyun. Existence and uniqueness of solutions to first-order three-point bound-ary value problems[J]. Applied Mathematics Letters, 2002, 15(2):211-216.
[13] LIU Bing. Existence and uniqueness of solutions to first-order multipoint boundary value problems[J]. Applied Mathematics Letters, 2004, 17(11):1307-1316.
[1] CHEN Bin, Abuelgasimalshaby Elzebir. Existence and multiplicity results for a second-order multi-point boundary value problem at resonance [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2016, 51(4): 49-52.
[2] ZHU Wen-wen. Existence and multiplicity of positive solutions of first order periodic boundary value problems with parameter [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2016, 51(12): 36-41.
[3] MA Lu-yi. The Ambrosetti-Prodi type results of the nonlinear second-order Neumann boundary value problem [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2015, 50(03): 62-66.
[4] SUN Yan-mei1, ZHAO Zeng-qin2. Existence of solutions for a class of second order  singular impulsive differential equations [J]. J4, 2013, 48(6): 91-95.
[5] LI Fan-fan, LIU Xi-ping*, ZHI Er-tao. Existence of a solution for the boundary value problem of
fractional differential equation with delay [J]. J4, 2013, 48(12): 24-29.
[6] ZHANG Xiang, HUANG Shu-xiang. Monotone iterative technique, existence and uniqueness results for the nonlinear fractional reaction-diffusion equation [J]. J4, 2011, 46(2): 9-14.
[7] HUANG Yu-mei,GAO De-zhi,QIN Wei,DONG Xin . Existence of three solutions for some second-order four-point boundary value problems [J]. J4, 2008, 43(6): 53-56 .
[8] TIAN Jia-cai and GAO Li . Multiple solutions for a class of second order differential equations [J]. J4, 2007, 42(6): 55-60 .
Viewed
Full text


Abstract

Cited
  Shared   
  Discussed   
No Suggested Reading articles found!
Copyright 2018 © Editorial office of JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE)
Supported by Beijing Magtech Co.Ltd