具偏差变元的二阶微分方程多个正解及其应用
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摘要
为了研究具偏差变元的二阶微分方程边值问题三个正解的存在性,首先给出了边值问题的格林函数表达式并研究了格林函数的性质。进而,利用Leggett-Williams不动点定理和Hlder不等式给出了存在3个正解的一些新的充分条件。最后,通过例子验证了主要结论的正确性。
To investigated the existence of three positive solutions of second order differential equations with deviating arguments.Firstly,the expression and properties of Green's function for the boundary value problem was investigated.Furthermore,we established some new sufficient conditions for the existence of three positive solutions by using Leggett-Williams' fixed point theorem and Hlder's inequality.Finally,an example was included to illustrate the main results.
To investigated the existence of three positive solutions of second order differential equations with deviating arguments.Firstly,the expression and properties of Green's function for the boundary value problem was investigated.Furthermore,we established some new sufficient conditions for the existence of three positive solutions by using Leggett-Williams' fixed point theorem and Hlder's inequality.Finally,an example was included to illustrate the main results.
引文
[1]JANKOWSKI T.Positive solutions for fourth-order differential equations with deviating arguments and integral boundary conditions[J].Nonlinear Analysis:Theory,Methods&Applications,2010,73(5):1289-1299.
[2]JANKOWSKI T,JANKOWSKI R.Multiple solutions of boundary-value problems for fourth-order differential equations with deviating arguments[J].Journal of Optimization Theory and Applications,2010,146(1):105-115.
[3]BAI Dingyong,XU Yuantong.Positive solutions of second-order two-delay differential systems with twinparameter[J].Nonlinear Analysis:Theory Methods&Applications,2005,63(4):601-617.
[4]BAI Dingyong,XU Yuantong.Existence of positive solutions for boundary value problem of second-order delay differential equations[J].Applied Mathematics Letters,2005,18(6):621-630.
[5]DU Bo,HU Xueping,GE Weigao.Positive solutions to a type of multipoint boundary value problem with delay and one-dimensional p-Laplacian[J].Applied Mathematics and Computation,2009,28(2):501-510.
[6]JIANG Daqing.Multiple positive solutions for boundary value problems of second-order delay differential equations[J].Applied Mathematics Letters,2007,15(5):575-583.
[7]WANG Weiping,SHEN Jianhua.Positive solutions to a multi-point boundary value problem with delay[J].AppliedMathematics and Computation,2007,188(1):96-102.
[8]WANG Youyu,ZHAO Wenxia,GE Weigao.Multiple positive solutions for boundary value problems of second order delay differential equations with one-dimensional p-Laplacian[J].Journal of Mathematical Analysis and Applications,2007,326(1):641-654.
[9]ZHANG Xuemei,FENG Meiqiang.Green’s function and positive solutions for a second-order singular boundary value problem with integral boundary conditions and a delayed argument[J].Abstract and Applied Analysis,2014:393187.
[10]MA Ruyun.Existence of positive solutions for a nonlinear m-point boundary value problem[J].ActaMathematicaSinica,2003,46(4):785-794.
[11]DU Zengji,KONG Lingju.Asymptotic solutions of singularly perturbed second-order differential equations and application to multi-point boundary value problems[J].Applied Mathematics Letters,2010,23(9):980-983.
[12]FENG Meiqiang,GE Weigao.Positive solutions for a class of m-point singular boundary value problems[J].Mathematical and Computer Modelling,2007,46(3/4):375-383.
[13]JANKOWSKI T.Solvability of three point boundary value problems for second order differential equations with deviating arguments[J].Journal of Mathematical Analysis and Applications,2005,312(2):620-636.
[2]JANKOWSKI T,JANKOWSKI R.Multiple solutions of boundary-value problems for fourth-order differential equations with deviating arguments[J].Journal of Optimization Theory and Applications,2010,146(1):105-115.
[3]BAI Dingyong,XU Yuantong.Positive solutions of second-order two-delay differential systems with twinparameter[J].Nonlinear Analysis:Theory Methods&Applications,2005,63(4):601-617.
[4]BAI Dingyong,XU Yuantong.Existence of positive solutions for boundary value problem of second-order delay differential equations[J].Applied Mathematics Letters,2005,18(6):621-630.
[5]DU Bo,HU Xueping,GE Weigao.Positive solutions to a type of multipoint boundary value problem with delay and one-dimensional p-Laplacian[J].Applied Mathematics and Computation,2009,28(2):501-510.
[6]JIANG Daqing.Multiple positive solutions for boundary value problems of second-order delay differential equations[J].Applied Mathematics Letters,2007,15(5):575-583.
[7]WANG Weiping,SHEN Jianhua.Positive solutions to a multi-point boundary value problem with delay[J].AppliedMathematics and Computation,2007,188(1):96-102.
[8]WANG Youyu,ZHAO Wenxia,GE Weigao.Multiple positive solutions for boundary value problems of second order delay differential equations with one-dimensional p-Laplacian[J].Journal of Mathematical Analysis and Applications,2007,326(1):641-654.
[9]ZHANG Xuemei,FENG Meiqiang.Green’s function and positive solutions for a second-order singular boundary value problem with integral boundary conditions and a delayed argument[J].Abstract and Applied Analysis,2014:393187.
[10]MA Ruyun.Existence of positive solutions for a nonlinear m-point boundary value problem[J].ActaMathematicaSinica,2003,46(4):785-794.
[11]DU Zengji,KONG Lingju.Asymptotic solutions of singularly perturbed second-order differential equations and application to multi-point boundary value problems[J].Applied Mathematics Letters,2010,23(9):980-983.
[12]FENG Meiqiang,GE Weigao.Positive solutions for a class of m-point singular boundary value problems[J].Mathematical and Computer Modelling,2007,46(3/4):375-383.
[13]JANKOWSKI T.Solvability of three point boundary value problems for second order differential equations with deviating arguments[J].Journal of Mathematical Analysis and Applications,2005,312(2):620-636.