TY - JOUR
A2 - Perera, Kanishka
AU - Kapula, Rajendra Prasad
AU - Murali, Penugurthi
AU - Rajendrakumar, Kona
PY - 2013
DA - 2013/09/09
TI - Existence of Positive Solutions for Higher Order -Laplacian Two-Point Boundary Value Problems
SP - 743943
VL - 2013
AB - 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]×ℝ2 to [0,∞), m1,n1,m2,n2∈ℕ 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.
SN - 1687-9643
UR - https://doi.org/10.1155/2013/743943
DO - 10.1155/2013/743943
JF - International Journal of Differential Equations
PB - Hindawi Publishing Corporation
KW -
ER -