International Journal of Differential Equations

Existence of Positive Solutions for Higher Order (p,q)-Laplacian Two-Point Boundary Value Problems

Rajendra Prasad Kapula, Penugurthi Murali, and Kona Rajendrakumar

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Abstract

We derive sufficient conditions for the existence of positive solutions to higher order (p,q)-Laplacian two-point boundary value problem, (-1)m1+n1-1[ϕp(u(2m1)(t))](n1)=f1(t,u(t),v(t)), t[0,1], (-1)m2+n2-1[ϕq(v(m2)(t))](2n2)=f2(t,u(t),v(t)), t[0,1], u(2i)(0)=0=u(2i)(1), i=0,1,2,,m1-1, [ϕp(u(2m1)(t))]at t=0(j)=0, j=0,1,,n1-2; [ϕp(u(2m1)(1))]=0, [ϕq(v(m2)(t))]at t=0(2i)=0=[ϕq(v(m2)(t))]at t=1(2i), i=0,1,,n2-1, v(j)(0)=0, j=0,1,2,,m2-2, and v(1)=0, where f1,f2 are continuous functions from [0,1]×2 to [0,), m1,n1,m2,n2 and 1/p+1/q=1. We establish the existence of at least three positive solutions for the two-point coupled system by utilizing five-functional fixed point theorem. And also, we demonstrate our result with an example.

Article information

Source
Int. J. Differ. Equ., Volume 2013 (2013), Article ID 743943, 9 pages.

Dates
Received: 17 April 2013
Revised: 17 July 2013
Accepted: 17 July 2013
First available in Project Euclid: 20 January 2017

Permanent link to this document
https://projecteuclid.org/euclid.ijde/1484881347

Digital Object Identifier
doi:10.1155/2013/743943

Mathematical Reviews number (MathSciNet)
MR3102796

Zentralblatt MATH identifier
1300.34056

Citation

Kapula, Rajendra Prasad; Murali, Penugurthi; Rajendrakumar, Kona. Existence of Positive Solutions for Higher Order $(p,q)$ -Laplacian Two-Point Boundary Value Problems. Int. J. Differ. Equ. 2013 (2013), Article ID 743943, 9 pages. doi:10.1155/2013/743943. https://projecteuclid.org/euclid.ijde/1484881347


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