一类变号三点边值问题正解的存在性

魏嘉　王静

摘要运用锥上的Guo-Krasnoselskijs不动点定理研究了一类非线性变号二阶三点边值问题至少一个正解的存在性.给出了与之相关联的线性二阶三点边值问题的格林函数及格林函数的一些性质.最后，作为应用，举例证明了所得结论的正确性.

关键词边值问题；变号；格林函数；正解

中图分类号O175文献标识码A文章编号1000-2537（2014）02-0072-06

参考文献：

[1]SUN J P， WEI J. Existence of positive solution for semipositone second-order three-point boundary-value problem [J]. Eletron J Diff Equ， 2008，41（1）：1-7.

[2]BAI D L， FENG H Y. Eigenvalue for a singular second order three-point boundary value problem [J]. J Appl Math Comp， 2012，38（1-2）：443-452.

[3]BAI Z B， DU Z J. Positive solutions for some second-order four-point boundary value problems [J]. J Math Anal Appl， 2007，330（1）：34-50.

[4]BOHNER M， STEVIC S. Linear perturbations of a nonoscillatory second-order dynamic equation [J]， J Diff Equ Appl， 2009，15（11）：1211-1221.

[5]DU X S， ZHAO Z Q. A necessary and sufficient condition for the existence of positive solutions to singular sublinear three-point boundary value problems[J]. J Appl Math Comp， 2007，186（1）：404-413.

[6]GUPTA C P. Solvability of a three-point nonlinear boundary value problem for a second order ordinary differential equations [J]. J Math Anal Appl， 1992，168 （2）：540-551.

[7]KONG L J. Second order singular boundary value problems with integral boundary conditions [J]. Nonlinear Anal， 2010，31（5）：2628-2638.

[8]KUN W， ZHI L. Positive solutions for a system of second-order boundary-value problems involving first-order derivatives [J]. Eletron J Diff Equ， 2012，135（1）：1-17.

[9]LI G， LIU X， JIA M. Positive solutions to a type of nonlinear three-point boundary-value problem with sign changing nonlinearities [J]. Comput Math Appl， 2009，57（3）：348-355.

[10]LIU B， LIU L， WU Y. Positive solutions for singular second order three-point boundary value problems [J]. Nonlinear Anal， 2007，66（12）：2756-2766.

[11]MA R. Positive solutions of a nonlinear three-point boundary value problems [J]. Electron J Differential Equations， 1998，34 （1）：1-8.

[12]申腾飞，刘文斌，宋文耀.一类带有p-Laplacian 算子分数阶微分方程边值问题正解的存在性[J].湖南师范大学自然科学学报， 2012，35（5）：9-14.

[13]GUO D， LAKSHMIKANTHAM V. Nonlinear problems in abstract cones [M]. New York：Academic Press， 1988.

[14]KRASNOSELSKIJ M A. Positive solutions of operator equations [M]. Groningen： Noordhoff， 1964.

（编辑沈小玲）

摘要运用锥上的Guo-Krasnoselskijs不动点定理研究了一类非线性变号二阶三点边值问题至少一个正解的存在性.给出了与之相关联的线性二阶三点边值问题的格林函数及格林函数的一些性质.最后，作为应用，举例证明了所得结论的正确性.

关键词边值问题；变号；格林函数；正解

中图分类号O175文献标识码A文章编号1000-2537（2014）02-0072-06

参考文献：

[1]SUN J P， WEI J. Existence of positive solution for semipositone second-order three-point boundary-value problem [J]. Eletron J Diff Equ， 2008，41（1）：1-7.

[2]BAI D L， FENG H Y. Eigenvalue for a singular second order three-point boundary value problem [J]. J Appl Math Comp， 2012，38（1-2）：443-452.

[3]BAI Z B， DU Z J. Positive solutions for some second-order four-point boundary value problems [J]. J Math Anal Appl， 2007，330（1）：34-50.

[4]BOHNER M， STEVIC S. Linear perturbations of a nonoscillatory second-order dynamic equation [J]， J Diff Equ Appl， 2009，15（11）：1211-1221.

[5]DU X S， ZHAO Z Q. A necessary and sufficient condition for the existence of positive solutions to singular sublinear three-point boundary value problems[J]. J Appl Math Comp， 2007，186（1）：404-413.

[6]GUPTA C P. Solvability of a three-point nonlinear boundary value problem for a second order ordinary differential equations [J]. J Math Anal Appl， 1992，168 （2）：540-551.

[7]KONG L J. Second order singular boundary value problems with integral boundary conditions [J]. Nonlinear Anal， 2010，31（5）：2628-2638.

[8]KUN W， ZHI L. Positive solutions for a system of second-order boundary-value problems involving first-order derivatives [J]. Eletron J Diff Equ， 2012，135（1）：1-17.

[9]LI G， LIU X， JIA M. Positive solutions to a type of nonlinear three-point boundary-value problem with sign changing nonlinearities [J]. Comput Math Appl， 2009，57（3）：348-355.

[10]LIU B， LIU L， WU Y. Positive solutions for singular second order three-point boundary value problems [J]. Nonlinear Anal， 2007，66（12）：2756-2766.

[11]MA R. Positive solutions of a nonlinear three-point boundary value problems [J]. Electron J Differential Equations， 1998，34 （1）：1-8.

[12]申腾飞，刘文斌，宋文耀.一类带有p-Laplacian 算子分数阶微分方程边值问题正解的存在性[J].湖南师范大学自然科学学报， 2012，35（5）：9-14.

[13]GUO D， LAKSHMIKANTHAM V. Nonlinear problems in abstract cones [M]. New York：Academic Press， 1988.

[14]KRASNOSELSKIJ M A. Positive solutions of operator equations [M]. Groningen： Noordhoff， 1964.

（编辑沈小玲）

摘要运用锥上的Guo-Krasnoselskijs不动点定理研究了一类非线性变号二阶三点边值问题至少一个正解的存在性.给出了与之相关联的线性二阶三点边值问题的格林函数及格林函数的一些性质.最后，作为应用，举例证明了所得结论的正确性.

关键词边值问题；变号；格林函数；正解

中图分类号O175文献标识码A文章编号1000-2537（2014）02-0072-06

参考文献：

[1]SUN J P， WEI J. Existence of positive solution for semipositone second-order three-point boundary-value problem [J]. Eletron J Diff Equ， 2008，41（1）：1-7.

[2]BAI D L， FENG H Y. Eigenvalue for a singular second order three-point boundary value problem [J]. J Appl Math Comp， 2012，38（1-2）：443-452.

[3]BAI Z B， DU Z J. Positive solutions for some second-order four-point boundary value problems [J]. J Math Anal Appl， 2007，330（1）：34-50.

[4]BOHNER M， STEVIC S. Linear perturbations of a nonoscillatory second-order dynamic equation [J]， J Diff Equ Appl， 2009，15（11）：1211-1221.

[5]DU X S， ZHAO Z Q. A necessary and sufficient condition for the existence of positive solutions to singular sublinear three-point boundary value problems[J]. J Appl Math Comp， 2007，186（1）：404-413.

[6]GUPTA C P. Solvability of a three-point nonlinear boundary value problem for a second order ordinary differential equations [J]. J Math Anal Appl， 1992，168 （2）：540-551.

[7]KONG L J. Second order singular boundary value problems with integral boundary conditions [J]. Nonlinear Anal， 2010，31（5）：2628-2638.

[8]KUN W， ZHI L. Positive solutions for a system of second-order boundary-value problems involving first-order derivatives [J]. Eletron J Diff Equ， 2012，135（1）：1-17.

[9]LI G， LIU X， JIA M. Positive solutions to a type of nonlinear three-point boundary-value problem with sign changing nonlinearities [J]. Comput Math Appl， 2009，57（3）：348-355.

[10]LIU B， LIU L， WU Y. Positive solutions for singular second order three-point boundary value problems [J]. Nonlinear Anal， 2007，66（12）：2756-2766.

[11]MA R. Positive solutions of a nonlinear three-point boundary value problems [J]. Electron J Differential Equations， 1998，34 （1）：1-8.

[12]申腾飞，刘文斌，宋文耀.一类带有p-Laplacian 算子分数阶微分方程边值问题正解的存在性[J].湖南师范大学自然科学学报， 2012，35（5）：9-14.

[13]GUO D， LAKSHMIKANTHAM V. Nonlinear problems in abstract cones [M]. New York：Academic Press， 1988.

[14]KRASNOSELSKIJ M A. Positive solutions of operator equations [M]. Groningen： Noordhoff， 1964.

（编辑沈小玲）