一类具有p-Laplace算子的非线性分数阶微分方程解的存在性与多解性
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摘要
利用Green函数的性质和锥上不动点定理研究一类具有p-Laplace算子的非线性分数阶微分方程边值问题解的存在性和多解性.
We studied the existence and multiplicity of solutions for a class of boundary value problems of nonlinear fractional differential equations with p-Laplacian operator by using the properties of Green's function and fixed-point theorems on cone.
We studied the existence and multiplicity of solutions for a class of boundary value problems of nonlinear fractional differential equations with p-Laplacian operator by using the properties of Green's function and fixed-point theorems on cone.
引文
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[7] GUO Limin,LIU Lishan,WU Yonghong.Existence of Positive Solutions for Singular Fractional Differential Equations with Infinite-Point Boundary Conditions[J].Nonlinear Anal:Model Control,2016,21(5):635-650.
[8] WANG Jinhua,XIANG Hongjun,LIU Zhigang.Positive Solutions for Three-Point Boundary Value Problems of Nonlinear Fractional Differential Equations with p-Laplacian[J].Far East J Appl Math,2009,37(1):33-47.
[9] LIU Xiping,JIA Mei,GE Weigao.The Method of Lower and Upper Solutions for Mixed Fractional Four-Point Boundary Value Problem with p-Laplacian Operator[J].Appl Math Lett,2017,65:56-62.
[10] JIA Mei,LIU Xiping.Multiplicity of Solutions for Integral Boundary Value Problems of Fractional Differential Equations with Upper and Lower Solutions[J].Appl Math Comput,2014,232:313-323.
[11] WANG Jinhua,XIANG Hongjun,LIU Zhigang.Existence of Concave Positive Solutions for Boundary Value Problem of Nonlinear Fractional Differential Equation with p-Laplacian Operator[J/OL].Int J Math Math Sci,2010-03-09.doi:10.1155/2010/495138.
[12] ZHANG Luchao,ZHANG Weiguo,LIU Xiping,et al.Existence of Positive Solutions for Integral Boundary Value Problems of Fractional Differential Equations with p-Laplacian[J/OL].Adv Difference Equ,2017-02-01.https://doi.org/10.1186/s13362-017-1086-5.
[2] Meral F C,Royston T J,Magin R.Fractional Calculus in Viscoelasticity:An Experimental Study[J].Commun Nonlinear Sci Numer Simul,2010,15(4):939-945.
[3] Kilbas A A,Srivastava H M,Trujillo J J.Theory and Applications of Fractional Differential Equations[M].Amsterdam:Elsevier,2006.
[4] Weitzner H,Zaslavsky G M.Some Applications of Fractional Equations[J].Commun Nonlinear Sci Numer Simul,2003,8(3/4):273-281.
[5] BAI Zhanbing,LHaishen.Positive Solutions for Boundary Value Problem of Nonlinear Fractional Differential Equation[J].J Math Anal Appl,2005,311(2):495-505.
[6] HAN Zhenlai,LU Hongling,SUN Shurong,et al.Positive Solutions to Boundary-Value Problems of p-Laplacian Fractional Differential Equations with a Parameter in the Buondary[J].Electron J Differential Equations,2012,213:1-14.
[7] GUO Limin,LIU Lishan,WU Yonghong.Existence of Positive Solutions for Singular Fractional Differential Equations with Infinite-Point Boundary Conditions[J].Nonlinear Anal:Model Control,2016,21(5):635-650.
[8] WANG Jinhua,XIANG Hongjun,LIU Zhigang.Positive Solutions for Three-Point Boundary Value Problems of Nonlinear Fractional Differential Equations with p-Laplacian[J].Far East J Appl Math,2009,37(1):33-47.
[9] LIU Xiping,JIA Mei,GE Weigao.The Method of Lower and Upper Solutions for Mixed Fractional Four-Point Boundary Value Problem with p-Laplacian Operator[J].Appl Math Lett,2017,65:56-62.
[10] JIA Mei,LIU Xiping.Multiplicity of Solutions for Integral Boundary Value Problems of Fractional Differential Equations with Upper and Lower Solutions[J].Appl Math Comput,2014,232:313-323.
[11] WANG Jinhua,XIANG Hongjun,LIU Zhigang.Existence of Concave Positive Solutions for Boundary Value Problem of Nonlinear Fractional Differential Equation with p-Laplacian Operator[J/OL].Int J Math Math Sci,2010-03-09.doi:10.1155/2010/495138.
[12] ZHANG Luchao,ZHANG Weiguo,LIU Xiping,et al.Existence of Positive Solutions for Integral Boundary Value Problems of Fractional Differential Equations with p-Laplacian[J/OL].Adv Difference Equ,2017-02-01.https://doi.org/10.1186/s13362-017-1086-5.