Positive solutions for three-point boundary value problem of fractional differential equation with p-laplacian operator

摘要

We investigate the existence of multiple positive solutions for three-point boundary value problem of fractional differential equation with p -Laplacian operator - D; t β (φ p (D; t α x)) (t) = h (t) f (t, x (t)), t ∈ (0,1), x (0) = 0, D; t γ x (1) = a D; t γ x, D; t α x (0) = 0, where D; t β, D; t α, D; t γ are the standard Riemann-Liouville derivatives with 1 < α ≤ 2, 0 < β ≤ 1, 0 < γ ≤ 1, 0 ≤ α - γ - 1, ∈ (0,1) and the constant a is a positive number satisfying a α - γ - 2 ≤ 1 - γ; p -Laplacian operator is defined as φ p (s) = | s | p - 2 s, p > 1. By applying monotone iterative technique, some sufficient conditions for the existence of multiple positive solutions are established; moreover iterative schemes for approximating these solutions are also obtained, which start off a known simple linear function. In the end, an example is worked out to illustrate our main results.