Abstract
In this paper, we establish the existence of positive solutions to a coupled system of higher order (p, q)-Laplacian two-point boundary value problem, by using Guo-Krasnosel’skii fixed point theorem for operators on a cone in a Banach space.
Highlights
In this paper, we establish the existence of positive solutions to a coupled system of higher order (p, q)-Laplacian two-point boundary value problem
We establish the existence of positive solutions to a coupled system of higher order (p, q)-Laplacian two-point boundary value problem, ( ) ( ) (−1)m1−1 φp u(2m1) (t) (n1) = λ f1(t, u(t), v(t)), t ∈[0,1], (−1)n2 −1 φq u(m2 ) (t)
In Part 4, we estimate the bounds of the Green functions which will be used in defining the positive operator
Summary
Differential equations governed by nonlinear differential operators have been widely studied by many researchers. We consider a coupled system of higher order (p, q)-Laplacian two-point boundary functions for the corresponding homogeneous BVPs. For n1 ≥ 2 let G(t, s) be the Green’s function of the BVP. For m2 ≥ 2, let H(t, s) be the Green’s function of the BVP, −x(m2 ) (t) =0, t ∈[0,1], x( j) (= 0) 0= , j 0,1, 2,⋅⋅⋅, m2 − 2, x= (1) 0, and after simple computation it can be obtained as m2 m2. Let Gn2 (t, s) be the Green’s function of the homogeneous BVP, (−1)n2 y(2n2 ) (t) = 0, t ∈[0,1], y(2i) (0)= 0= y(2i) (1), i= 0,1,⋅⋅⋅, n2 −1, and it can be recursively defined as. In Part 4, we estimate the bounds of the Green functions which will be used in defining the positive operator. Let reader to [13]
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