scholarly journals Multiple Positive Solutions for Nonlinear Semipositone Fractional Differential Equations

2012 ◽  
Vol 2012 ◽  
pp. 1-10 ◽  
Author(s):  
Wen-Xue Zhou ◽  
Ji-Gen Peng ◽  
Yan-Dong Chu
Keyword(s):  
Differential Equations ◽  
Boundary Value Problem ◽  
Real Number ◽  
Positive Solutions ◽  
Fractional Differential Equations ◽  
Boundary Value ◽  
Multiple Positive Solutions ◽  
Fractional Boundary Value Problem ◽  
Fractional Differential ◽  
Multiplicity Of Positive Solutions

We present some new multiplicity of positive solutions results for nonlinear semipositone fractional boundary value problemD0+αu(t)=p(t)f(t,u(t))-q(t),0<t<1,u(0)=u(1)=u'(1)=0, where2<α≤3is a real number andD0+αis the standard Riemann-Liouville differentiation. One example is also given to illustrate the main result.

Multiple positive solutions of nonlinear fractional differential equations with integral boundary value conditions

2014 ◽  
Vol 17 (3) ◽  
Author(s):  
Wei Sun ◽  
Youyu Wang
Keyword(s):  
Differential Equations ◽  
Boundary Value Problem ◽  
Positive Solutions ◽  
Fractional Differential Equations ◽  
Boundary Value ◽  
Sufficient Conditions ◽  
Integral Boundary Conditions ◽  
Multiple Positive Solutions ◽  
Integral Boundary ◽  
Fractional Differential

AbstractIn this paper, we consider the multiplicity of positive solutions for a class of nonlinear boundary-value problem of fractional differential equations with integral boundary conditions. By means of a fixed point theorem due to Avery and Peterson, we provide sufficient conditions for the existence of multiple positive solutions to the integral boundary value problem.

scholarly journals Singular Positone and Semipositone Boundary Value Problems of Nonlinear Fractional Differential Equations

2009 ◽  
Vol 2009 ◽  
pp. 1-17 ◽  
Author(s):  
Chengjun Yuan ◽  
Daqing Jiang ◽  
Xiaojie Xu
Keyword(s):  
Differential Equations ◽  
Boundary Value Problem ◽  
Fractional Derivative ◽  
Real Number ◽  
Fractional Differential Equations ◽  
Boundary Value ◽  
Existence Results ◽  
Fractional Boundary Value Problem ◽  
Liouville Fractional Derivative ◽  
Fractional Differential

We present some new existence results for singular positone and semipositone nonlinear fractional boundary value problemD0+αu(t)=μa(t)f(t,u(t)), 0<t<1,u(0)=u(1)=u′(0)=u′(1)=0, whereμ>0,a,andfare continuous,α∈(3,4]is a real number, andD0+αis Riemann-Liouville fractional derivative. Throughout our nonlinearity may be singular in its dependent variable. Two examples are also given to illustrate the main results.

scholarly journals Existence and Multiple Positive Solutions for Boundary Value Problem of Fractional Differential Equation withp-Laplacian Operator

2014 ◽  
Vol 2014 ◽  
pp. 1-18 ◽  
Author(s):  
Min Jiang ◽  
Shouming Zhong
Keyword(s):  
Differential Equations ◽  
Boundary Value Problem ◽  
Positive Solution ◽  
Positive Solutions ◽  
Fractional Differential Equations ◽  
Boundary Value ◽  
Laplacian Operator ◽  
Multiple Positive Solutions ◽  
Fractional Differential ◽  
Fixed Point Techniques

This paper investigates the existence, multiplicity, nonexistence, and uniqueness of positive solutions to a kind of two-point boundary value problem for nonlinear fractional differential equations withp-Laplacian operator. By using fixed point techniques combining with partially ordered structure of Banach space, we establish some criteria for existence and uniqueness of positive solution of fractional differential equations withp-Laplacian operator in terms of different value of parameter. In particular, the dependence of positive solution on the parameter was obtained. Finally, several illustrative examples are given to support the obtained new results. The study of illustrative examples shows that the obtained results are applicable.

scholarly journals Existence of multiple positive solutions for semipositone fractional boundary value problems

Filomat ◽  
2019 ◽  
Vol 33 (3) ◽  
pp. 749-759 ◽  
Author(s):  
Şerife Ege ◽  
Fatma Topal
Keyword(s):  
Boundary Value Problems ◽  
Positive Solutions ◽  
Fractional Differential Equations ◽  
Boundary Value ◽  
Multiple Positive Solutions ◽  
Point Boundary ◽  
Existence And Multiplicity ◽  
Fractional Differential ◽  
Multiplicity Of Positive Solutions ◽  
Fractional Boundary Value Problems

In this paper, we study the existence and multiplicity of positive solutions to the four-point boundary value problems of nonlinear semipositone fractional differential equations. Our results extend some recent works in the literature.

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