Vol. 40 No Journal of Jiangxi Normal University Natural Science Jul. 2016

Transcript

1 4 4 Vol 4 No Journal of Jiangxi Normal Universiy Naural Science Jul O 77 9 A DOI 6357 /j cnki issn C q x' x /q G s = { α 2 - s -9 2 β 2 2 s α 2 - s β 2 - s 2 - s G s q G s s q = β 2 / 2 { x φ f x x' = P = x C q q x x x 2 x = x' = x P C q αx' βx = 3 x P x = x α β > φ 4 φ C R φ s ds < = = 7! F = G s φ s ds F P 7 ~ Ω Banach E q = β 2 / 2 C q = x R x x' q x' <! x P E E θ Ω A Ω P P λax x x Ω P λ i A Ω P P = C q C q 6 Ω Banach E x = x x 2 x = x 2 = q x' P E A Ω P P Ax /x x Ω P / C q Banach x i A Ω P P =

2 35 26! H 2 g C!!! f x y g x q y x y! -!! H 3 c/ [ ( c! s) g x z ] > φ s d x c z c H 4 g C! -!!! f x y g x y x y! -!! lim g x y /x =! y x! H 5 g 2 C! -!!! f x y g 2 x y x y! -!! limg 2 x y /x =! y x x P A Ax = G s φ s f s x s x' s ds H H 2 A P P Ax = s φ s f s x s x' s ds G s φ s g x s q s x' s ds G g c c' <! φ s ds c x c' x q Ax ' = q α - s ( β ) φ s f s x s x' s ds - - s φ s f s x s x' s ds α - s β φ s f s x s x' s ds φ s f s x s x' s ds 2 φ s f s x s x' s ds Ax ' - Ax ' = 2 φ s ds g c c' <! lim x n = x lim x n ' = n! n! c x c' x x Ax ' f x n x n ' g x n 4 A P P q x n ' g x y x M y M α - s β φ s f s x s x' s ds - H φ C L φ > f C! -!! - s φ s f s x s x' s ds α - s β α β φ s f s x s x' s ds - s φ s f s x s x' s ds ( c x c' x c x c' x g c c' ) - Ax ' - Ax ' = α - s β φ s ds g c c' - s φ s ds α - s β φ s f s x s x' s ds - - s φ s f s x s x' s ds - α - s ( β - s) φ s f s x s x' s ds = α - s β α - s ( - - ) φ s f s x s x' s ds - - s φ s f s x s x' s ds = β - s αs - - s φ s f s x s x' s ds - - s φ s f s x s x' s ds = αs - - s φ s f s x s x' s ds - - s φ s f s x s x' s ds αs - - s - αs φ s f s φ s f s x s x' s ds x s x' s ds αs - - s φ s f s x s x' s ds Ax C x n P x P lim x n = x M > n! x n < M n 2 3

3 n! Ax n - Ax G s φ s f s x n s x n ' s f s x s = x ' s ds φ s f s x n s x n ' s f s x s x ' s ds Ax n - Ax 2 = Ax - Ax 2 ( q α - s β - - s φ s f s x m x n ' f s x x ' ds ε > δ > 2 - < δ α - s β ( ) φ s f s x n x n ' f s x x ' ds q [ ( s - αs Ax ' 2 < ε Ax x D Ax - Ax 2 < ε Ax ' - ) φ s Ax ' x D f s x n x n ' - f s x x ' ds ( - αs ) φ s Arzela-Ascoli A D C f s x n x n ' - f s x x ' d s ] Ax Ax = Ax A P P Ax ' D M > x D A P P x M H ~ H 4 Ax = 2 G s φ s f s x s H 3 R > x' s ds φ s ds g x y R / ( x M y M g x y φ s ds x R y R ) > 2 Ax 2 2 φ s ds g x y C q Ω = x C q x M y M x < R A D C q C μax x μ x P Ω 2 < 2 x D μ x P Ω G s - μ Ax = x x Ax = G s φ s f s G 2 s φ s d s ) Ax ' - Ax ' 2 = g x y x M y M α - s β φ s f s x s x' s ds - - s φ s f s x s x' s ds α 2 - s β 2 φ s f s x s x' s ds - s φ s f s x s x' s ds = - 2 ( - αs α ) β φ s f s - s φ s f s x s x' s ds - s φ s f s x s x' s ds - - s φ s f s x s x' s ds = x s x' s ds 2-2 ( - αs ) φ s f s x s x' s ds 2 - φ s f s x s x' s ds 2 - s φ s f s x s x' s ds ( φ s ds 2 φ s d s ) g x y x M y M x s x ' s ds G s φ s ds g x y y R x R g x y q x ' = u q φ s ds x R y R Ax ' φ s ds g x y x R y R R = x x 2 φ s ds g x y x R y R R / g x y φ s ds x R y R 2 5 i A Ω P P = 3 < a * < b * < N * = βa ( * 2 min a * b b* s φ s d s) * 2 a * G - H 4 R 2 ' > R g x y N * x

4 x R 2 ' y -!! R 2 = 2 α N ** x x R 3 y -!! C q β R 2 ' / βa * 2 R 2 > R C q Ω 3 = x C q x < R 3 Ω 2 = x C q x < R 2 Ax /x Ax /x x P Ω 3 x P Ω 2 x P Ω 2 x Ax a * b * x q x βa * 2 x / 2 = βa * 2 2 R 2 2 ' = R 2 ' βa * 2 x Ax = G s φ s f s x s b x ' s ds * G s φ s g x s x ' s ds a * b* G s φ s N * x s ds N * b R 2 ' a * G s φ s ds * a * i A Ω 2 \ Ω P P = i A Ω 2 P P i A Ω P P = - 5 A Ω 2 \ Ω P 2 μ x 2 H ~ H 槡 x' 5 2 x b = x = x' = < R < αx' βx = R 2 C q Ω Ω 2 = x C q x < R = x C q x < R A Ω 2 \ Ω P < a ** < b ** < N ** = βa ( **2 min b** b** G s φ s d s) 2 H 5 R 3 - < R g 2 x y x P Ω 3 x Ax a ** b ** x q x βa **2 x / 2 = βa **2 R 3 / 2 x Ax = x ' s ds b** b** G s φ s N ** x s ds N ** β2 2 R 3 b** G s φ s f s x s G s φ s g 2 x s x ' s ds G s φ s ds N * R 2 ' min a * b b* G s φ s ds = * a * N * βa * 2 R 2 ' 2 min a * b b* N ( G s φ s d s ) 2 R 3 min a * b b** G s φ s ds > R 3 * * a * 2 2 α x β x > R 3 > R βa * 2 βa * 2 2 ' 6 x x > 2 R 2 ' / βa * 2 = i A Ω 3 P P = 6 R 2 x < R 2 6 i A Ω 2 P P = i A Ω \ Ω 3 P P = i A Ω P P i A Ω 3 P P = A Ω \ Ω 3 P A P P 3 A Ω P 2 2 a β > α a > b > μ > 7 μ < c / π c a c b 8 c! φ = μ / - 槡 f x y = 2 y /4 a x b H g x z = z a x b f x y g x q y H 2

5 c! c! c! c / φ s ds c / μπ x c y c x c y c g x y = y a x b = c / μπ c a c b 8 c! c / φ s ds x c y c g x y > H 3 4 Wei Zhongli Some necessary and sufficien condiions for g x y = g 2 x y = x b f x y exisence of posiive soluions for hird order singular sublinear muli-poin boundary value problems J Aca g x y = g 2 x y lim g x y /x = lim x b /x =! Mah Sci x! x! limg 2 x y /x = lim x b 5 Zhang Haie Sun Jianping Exisence and ieraion of monoone posiive soluions for hird-order nonlocal BVPs in- /x =! x x y -!! H 4 H 5 volving inegral condiions J Elecronic Journal of Qualiaive Theory of Differenial Equaions J 7 Agarwal Ravi P O Regan Donal Yan Baoqiang Muliple 3 posiive soluions of singular Dirichle second-order boundary-value problems wih derivaive dependence J Journal of Dynamical and Conrol Sysems Li Yongxiang Shang Yaya An exisence resul of posiive 3 soluions for fully second-order boundary value problems H ~ H 4 J Journal of Funcion Spaces doi 55 /25 / x 9 Zhang Guowei Posiive soluions of wo-poin boundary Ω P x value problems for second-order differenial equaions wih R q he nonlineariy dependen on he derivaive J Nonlinear Anal x ' R x 2 Ω 2 \ Ω P R x 2 R 2 Mousafa El-Shahed Posiive soluions for nonlinear singular hird order boundary value problem J Communica- R q x 2 ' R 2 ions in Nonlinear Science and Numerical Simulaion 2 H ~ H J x Ω \ Ω 3 P R x R R 3 q x ' R M x 2 Ω 2 \ Ω P 27 3 M 4 Cheng Ming Nagumo heorems of hird-order singular nonlinear boundary value problems J Boundary Value Problems 25-2 Kelevedjiev P Popivanov N Bekesheva L Exisence of soluions for a class of hird-order nonlinear boundary value problem C AIP Conference Proceedings doi 63 / Wei Zhongli Some necessary and sufficien condiions for exisence of posiive soluions for hird order singular er-linear muli-poin boundary value problems J J Appl Mah Compu Deimling K Nonlinear funcional analysis M Berlin Springer-Verlag M

6 J CAT J J Chang Hua-Hua Qian Jiahe Ying Zhiliang Alpha-sraified mulisage compuerized adapive esing J Applied Psychological Measuremen J J J J The Iem Selecion Sraegy of Raising Iem Pool Securiy HE Xiang LUO Fen GAN Dengwen * DING Shuliang WANG Wenyi College of Compuer Informaion and Engineering Jiangxi Normal Universiy Nanchang Jiangxi 3322 China Absrac The safey of iem pool is he key poin o he implemenaion of compuerized adapive es inspired by he original dynamic a-sraified mehod and mean inequaliy consrucing anoher iem selecion sraegy of he dynamic a-sraified The simulaion experimenal resuls showed ha he new iem selecion sraegy o keep he es precision of he original dynamic a-sraified mehod and furher improves he securiy of he es Key words iem informaion discriminaion iem selecion sraegy 353 The Posiive Soluions of a Class of Third-Order Boundary-Value Problems wih Derivaive Dependence LI Fengyan SHI Jinchuan 2 Deparmen of Business and Trade College of Liaoning Adminisraion Shenyang Liaoning 6 China 2 Keya College Shenyang Universiy of Chemical Technology Shenyang Liaoning 67 China Absrac By means of he mehods of fixed poin index compuaion he exisence of posiive soluions of a class of hird-order boundary-value problems wih derivaive dependence is proved The boundary-value problems considered possess differen order boundary condiions and singulariy from hose in previous works An example is given o apply he resuls obained Key words derivaive dependence hird-order boundary-value posiive soluion