非局部高阶分数微分方程正解的唯一性
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摘要
应用广义α-凹算子的不动点理论,得到了保证方程正解的存在和唯一性的标准,同时研究了方程解对参数的依赖性,研究了一类分数阶微分方程非局部边值问题正解的存在唯一性.
In this paper,we consider the uniqueness of positive solutions mr fractional differential equation multi—point boundary value problem with boundary conditions involving a positive parameter. By using a fixed point theorem of generalα—concave operators,we present criteria which guarantee the existence and uniqueness of a positive solution The dependence of the solution on the parameter λ is also studied.
In this paper,we consider the uniqueness of positive solutions mr fractional differential equation multi—point boundary value problem with boundary conditions involving a positive parameter. By using a fixed point theorem of generalα—concave operators,we present criteria which guarantee the existence and uniqueness of a positive solution The dependence of the solution on the parameter λ is also studied.
引文
[1]BAI Z,LüL.Positive solutions fnr boundary value problem of nonlinear fl'actional differential equation,J Math Anal Appl 2005(311):495—505.
[2]BENCHOHRA M,HAMANI S,NTOUYAS S K.Boundary value problems fnr differential equations with fractional order and nonlocal conditions,Nonlinear Anal 2009(71):2391—2396.
[3]E1-SHAHED M,NIETO J J.Nontrivial solutions fnr a nonlinear multi—point boundary value problem of fractional order,Comput Math Appl 2010(59):3438—3443.
[4]GOODEICH C S.Existence of a positive solution to a class of fractional differential equations,App Math Lett 2010(23):1050—1055.
[5]GOODEICH C S.Existence and uniqueness of solutions to a fractional difference equation with nonlocal conditions,Comput Math Appl 2011(61):191—202.
[6]GOODEICH C S.Existence of a positive solution to systems of differential equations of fractional order,Comput Math Appl 2011(62):1251—1268.
[7]REHMAN M.KHAN R A.Existence and uniqueness of solutions fnr multi—point boundary value problems fnr fl'actional differential equations,Appl Math Lett 2010(23):1038—1044.
[8]XU J,WEI Z,DONG W.Uniqueness of positive solutions fnr a class of fractional boundary value problems,Appl Math Lett 2012(25):590—593.
[9]ZHANG X.HAN Y.Existence and uniqueness of positive solutions fnr higher order nonlocal fractional differential equations,Appl Math Lett 2012(25):555—560.
[10]ZHONG W,LIN W.Nonlocal and multiple_point boundary value problem fnr fractional differential equations,Comput Math Appl 2010(59):1345—1351.
[11]ZHAI C,YANG C,GUO C.Positive solutions of operator equation on ordered Banach spaces and applications,Comput Math Appl 2008(56):3150—3156.
[2]BENCHOHRA M,HAMANI S,NTOUYAS S K.Boundary value problems fnr differential equations with fractional order and nonlocal conditions,Nonlinear Anal 2009(71):2391—2396.
[3]E1-SHAHED M,NIETO J J.Nontrivial solutions fnr a nonlinear multi—point boundary value problem of fractional order,Comput Math Appl 2010(59):3438—3443.
[4]GOODEICH C S.Existence of a positive solution to a class of fractional differential equations,App Math Lett 2010(23):1050—1055.
[5]GOODEICH C S.Existence and uniqueness of solutions to a fractional difference equation with nonlocal conditions,Comput Math Appl 2011(61):191—202.
[6]GOODEICH C S.Existence of a positive solution to systems of differential equations of fractional order,Comput Math Appl 2011(62):1251—1268.
[7]REHMAN M.KHAN R A.Existence and uniqueness of solutions fnr multi—point boundary value problems fnr fl'actional differential equations,Appl Math Lett 2010(23):1038—1044.
[8]XU J,WEI Z,DONG W.Uniqueness of positive solutions fnr a class of fractional boundary value problems,Appl Math Lett 2012(25):590—593.
[9]ZHANG X.HAN Y.Existence and uniqueness of positive solutions fnr higher order nonlocal fractional differential equations,Appl Math Lett 2012(25):555—560.
[10]ZHONG W,LIN W.Nonlocal and multiple_point boundary value problem fnr fractional differential equations,Comput Math Appl 2010(59):1345—1351.
[11]ZHAI C,YANG C,GUO C.Positive solutions of operator equation on ordered Banach spaces and applications,Comput Math Appl 2008(56):3150—3156.