一類變號(hào)三點(diǎn)邊值問(wèn)題正解的存在性

魏嘉　王靜

摘要運(yùn)用錐上的Guo-Krasnoselskijs不動(dòng)點(diǎn)定理研究了一類非線性變號(hào)二階三點(diǎn)邊值問(wèn)題至少一個(gè)正解的存在性.給出了與之相關(guān)聯(lián)的線性二階三點(diǎn)邊值問(wèn)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(wèn)題；變號(hào)；格林函數(shù)；正解

中圖分類號(hào)O175文獻(xiàn)標(biāo)識(shí)碼A文章編號(hào)1000-2537（2014）02-0072-06

參考文獻(xiàn)：

[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(wèn)題正解的存在性[J].湖南師范大學(xué)自然科學(xué)學(xué)報(bào)， 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(yùn)用錐上的Guo-Krasnoselskijs不動(dòng)點(diǎn)定理研究了一類非線性變號(hào)二階三點(diǎn)邊值問(wèn)題至少一個(gè)正解的存在性.給出了與之相關(guān)聯(lián)的線性二階三點(diǎn)邊值問(wèn)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(wèn)題；變號(hào)；格林函數(shù)；正解

中圖分類號(hào)O175文獻(xiàn)標(biāo)識(shí)碼A文章編號(hào)1000-2537（2014）02-0072-06

參考文獻(xiàn)：

[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(wèn)題正解的存在性[J].湖南師范大學(xué)自然科學(xué)學(xué)報(bào)， 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(yùn)用錐上的Guo-Krasnoselskijs不動(dòng)點(diǎn)定理研究了一類非線性變號(hào)二階三點(diǎn)邊值問(wèn)題至少一個(gè)正解的存在性.給出了與之相關(guān)聯(lián)的線性二階三點(diǎn)邊值問(wèn)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(wèn)題；變號(hào)；格林函數(shù)；正解

中圖分類號(hào)O175文獻(xiàn)標(biāo)識(shí)碼A文章編號(hào)1000-2537（2014）02-0072-06

參考文獻(xiàn)：

[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(wèn)題正解的存在性[J].湖南師范大學(xué)自然科學(xué)學(xué)報(bào)， 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）