Existence of a Positive Solution for Nonlinear Differential Equations

International Journal of Mathematics Trends and Technology (IJMTT)
© 2016 by IJMTT Journal
Volume-36 Number-3
Year of Publication : 2016
Authors : G.U.Pawar, J.N.Salunke


G.U.Pawar, J.N.Salunke "Existence of a Positive Solution for Nonlinear Differential Equations", International Journal of Mathematics Trends and Technology (IJMTT). V36(3)137-139 August 2016. ISSN:2231-5373. www.ijmttjournal.org. Published by Seventh Sense Research Group.

In this paper, we prove the existence result for nonlinear differential equation without using themonotonocity of upper and lower solutions.

[1] Podlubny I.,Fractional Differential Equations.Academic Press,San Diego(1999).
[2] Wang C, Wang R.,Wang S.Yang C., Positive Solution of Singular Boundary Value Problems for a Nonlinear Fractional Differential Equation, Bound.Value Probl.(2011), Art ID 297026.
[3] J.N.Nanware, Existence Result for Nonlinear initial value problems involving the Difference of two two Monotone functions. Inter. Jour. Anal. Appl., Volume 7, Number 2(2015),179-184.
[4] Zhang S. The existence of a positive solution for a fractional differential equation , J.Math.Anal.Appl. 252(2000),804-812.
[5] A.A. Kilbas, H.M.Srivastava, and J.J.Trujillo, Theory and Applications of Fractional Differential Equation , North Holland Studies. Vol.204. Elsevier(North Holland) Science Publishers,Amsterdam,2006.
[6] Delbosco D.,Rodino L.,Existence and Uniqueness for a nonlinear fractional differential equation,J.Math,Anal.Appl.204(1996),609-625.
[7] Bai Z.B., Qiu T.T. , Existence of Positive solution for a singular fractional differential equation, Appl. Math. Comput.215(2009),2761-2767.
[8] J.N.Nanware, D.B.Dhaigude, Monotone Iterative Scheme for system of Riemann-Liouville Fractional Differential Equations with Integral Boundary Conditions. Math.Modelling Science Computation, Springer- Verlag,283(2012) 395-402
[9] M.M. Matar, On Existence of Positive solution for initial value problem on Nonlinear Fractional Differential Equations of order , Acta.Math.Univ.Comenianae vol.LXXXIV , 1(2015), PP 51-57.

Fractional Differential Equation (FDE), Upper and Lower Control Functions.