一類變號三點邊值問題正解的存在性
2014-10-22 12:28:56魏嘉王靜
湖南師范大學(xué)學(xué)報·自然科學(xué)版 2014年2期
魏嘉 王靜
摘要運用錐上的Guo-Krasnoselskijs不動點定理研究了一類非線性變號二階三點邊值問題至少一個正解的存在性.給出了與之相關(guān)聯(lián)的線性二階三點邊值問題的格林函數(shù)及格林函數(shù)的一些性質(zhì).最后，作為應(yīng)用，舉例證明了所得結(jié)論的正確性.
關(guān)鍵詞邊值問題；變號；格林函數(shù)；正解
中圖分類號O175文獻標(biāo)識碼A文章編號1000-2537（2014）02-0072-06
參考文獻：
[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]申騰飛，劉文斌，宋文耀.一類帶有p-Laplacian 算子分?jǐn)?shù)階微分方程邊值問題正解的存在性[J].湖南師范大學(xué)自然科學(xué)學(xué)報， 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.
（編輯沈小玲）
摘要運用錐上的Guo-Krasnoselskijs不動點定理研究了一類非線性變號二階三點邊值問題至少一個正解的存在性.給出了與之相關(guān)聯(lián)的線性二階三點邊值問題的格林函數(shù)及格林函數(shù)的一些性質(zhì).最后，作為應(yīng)用，舉例證明了所得結(jié)論的正確性.
關(guān)鍵詞邊值問題；變號；格林函數(shù)；正解
中圖分類號O175文獻標(biāo)識碼A文章編號1000-2537（2014）02-0072-06
參考文獻：
[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]申騰飛，劉文斌，宋文耀.一類帶有p-Laplacian 算子分?jǐn)?shù)階微分方程邊值問題正解的存在性[J].湖南師范大學(xué)自然科學(xué)學(xué)報， 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.
（編輯沈小玲）
摘要運用錐上的Guo-Krasnoselskijs不動點定理研究了一類非線性變號二階三點邊值問題至少一個正解的存在性.給出了與之相關(guān)聯(lián)的線性二階三點邊值問題的格林函數(shù)及格林函數(shù)的一些性質(zhì).最后，作為應(yīng)用，舉例證明了所得結(jié)論的正確性.
關(guān)鍵詞邊值問題；變號；格林函數(shù)；正解
中圖分類號O175文獻標(biāo)識碼A文章編號1000-2537（2014）02-0072-06
參考文獻：
[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]申騰飛，劉文斌，宋文耀.一類帶有p-Laplacian 算子分?jǐn)?shù)階微分方程邊值問題正解的存在性[J].湖南師范大學(xué)自然科學(xué)學(xué)報， 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.
（編輯沈小玲）
