Positive Solutions for Three-Point Boundary Value Problem of Fractional Differential Equation with p-Laplacian Operator

Abstract EN

We investigate the existence of multiple positive solutions for three-point boundary value problem of fractional differential equation with p-Laplacian operator -?tβ(φp(?tαx))(t)=h(t)f(t,x(t)), t∈(0,1), x(0)=0,?tγx(1)=a?tγx(ξ),?tαx(0)=0, where ?tβ,?tα,?tγ are the standard Riemann-Liouville derivatives with 1<α≤2,0<β≤1,0<γ≤1,0≤α−γ−1, ξ∈(0,1) and the constant a is a positive number satisfying aξα-γ-2≤1-γ; p-Laplacian operator is defined as φp(s)=|s|p-2s, 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.