In this paper,we study a Dirichlet-type boundary value problem(BVP) of nonlinear fractional differential equation with an order α∈(3,4],where the fractional derivative D~α_(o^+)is the standard Riemann-Liouville fra...In this paper,we study a Dirichlet-type boundary value problem(BVP) of nonlinear fractional differential equation with an order α∈(3,4],where the fractional derivative D~α_(o^+)is the standard Riemann-Liouville fractional derivative.By constructing the Green function and investigating its properties,we obtain some criteria for the existence of one positive solution and two positive solutions for the above BVP.The Krasnosel'skii fixedpoint theorem in cones is used here.We also give an example to illustrate the applicability of our results.展开更多
This paper investigates thc existence of positive solutions of the m-point boundary value problem for second-order dynamic equations on time scales, and obtain the result that the problem has at least one positive sol...This paper investigates thc existence of positive solutions of the m-point boundary value problem for second-order dynamic equations on time scales, and obtain the result that the problem has at least one positive solution by using functional-type cone expansion-compression fixed point theorem.展开更多
In this paper,we establish sufficient conditions for the existence of positive solutions to a general class of integral boundary value problem(BVP) of nonlinear fractional functional differential equation.A differenti...In this paper,we establish sufficient conditions for the existence of positive solutions to a general class of integral boundary value problem(BVP) of nonlinear fractional functional differential equation.A differential operator is taken in the RiemannLiouville sense.Our analysis relies on the Krasnosel’skii fixed-point theorem in cones.We also give examples to illustrate the applicability of our results.展开更多
In this paper, using two fixed-point theorems, we consider the existence and mul- tiplicity results of solutions to a nonlinear two point boundary value problem. In argument, the properties of the Green function play ...In this paper, using two fixed-point theorems, we consider the existence and mul- tiplicity results of solutions to a nonlinear two point boundary value problem. In argument, the properties of the Green function play an important role.展开更多
In this paper, we are concerned with the existence of positive solutions to the superlinear semipositone problem of the nth-order delayed differential system. The main result in this paper generalizes the correspondin...In this paper, we are concerned with the existence of positive solutions to the superlinear semipositone problem of the nth-order delayed differential system. The main result in this paper generalizes the corresponding result on the second order de-layed differential equation. Our proofs are based on the well-known Guo-Krasnoselskii fixed-point theorem.展开更多
基金Supported by the Research Fund for the Doctoral Program of High Education of China(20094407110001)Supported by the NSF of Guangdong Province(10151063101000003)
文摘In this paper,we study a Dirichlet-type boundary value problem(BVP) of nonlinear fractional differential equation with an order α∈(3,4],where the fractional derivative D~α_(o^+)is the standard Riemann-Liouville fractional derivative.By constructing the Green function and investigating its properties,we obtain some criteria for the existence of one positive solution and two positive solutions for the above BVP.The Krasnosel'skii fixedpoint theorem in cones is used here.We also give an example to illustrate the applicability of our results.
基金The Project Sponsored by the Scientific Research Foundation for the Returned 0verseas Chinese Scholars, State Education Ministry of China （48371109） and the Natural Science Foundation of Hebei Province of China （A2004000089）
文摘This paper investigates thc existence of positive solutions of the m-point boundary value problem for second-order dynamic equations on time scales, and obtain the result that the problem has at least one positive solution by using functional-type cone expansion-compression fixed point theorem.
基金Supported by the Natural Science Foundation of Guangdong Province(10151063101000003)
文摘In this paper,we establish sufficient conditions for the existence of positive solutions to a general class of integral boundary value problem(BVP) of nonlinear fractional functional differential equation.A differential operator is taken in the RiemannLiouville sense.Our analysis relies on the Krasnosel’skii fixed-point theorem in cones.We also give examples to illustrate the applicability of our results.
基金the National Natural Science Foundation of China(No.11271235)the Foundation of Datong University(XJY-2012211)The Development Foundation of Higher Education of Shanxi Province(ZJ-12001)
文摘In this paper, using two fixed-point theorems, we consider the existence and mul- tiplicity results of solutions to a nonlinear two point boundary value problem. In argument, the properties of the Green function play an important role.
基金National Natural Science Foundation of China (10671069)Shanghai LeadingAcademic Discipline Project (B407).
文摘In this paper, we are concerned with the existence of positive solutions to the superlinear semipositone problem of the nth-order delayed differential system. The main result in this paper generalizes the corresponding result on the second order de-layed differential equation. Our proofs are based on the well-known Guo-Krasnoselskii fixed-point theorem.
