Multiplicity of Positive Solutions for Fractional Differential Equation with p-Laplacian Boundary Value Problems

摘要

We investigate the existence of multiple positive solutions of fractional differential equations with p-Laplacian operator D_(a~+)~β+(φ_p(D_(a~+)~αu(t))) = f(t,u(t)), a < t < b, u~(j)(a) = 0, j = 0,1,2,...,n - 2, u~(α1)(b) = ξu~(α_1)(η), φ_p(D_(a~+)~αu(a)) = 0 = D_(a~+)~(β_1)(φ_p(D_(a~+)~αu(b))), where β ∈ (1,2], α ∈ (n - 1,n], n ≥ 3, ξ ∈ (0,∞), η ∈ (a,b), β_1 ∈ (0,1], α_1 ∈ {1,2,...,α - 2} is a fixed integer, and φ_p(s) = |s|~(p-2)s, p > 1, φ_p~(-1) = φ_q, (1/p) + (1/q) = 1, by applying Leggett-Williams fixed point theorems and fixed point index theory.