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Positive solutions for three-point boundary value problem of fractional differential equation with p-Laplacian operator. (English) Zbl 1267.35245
Summary: 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)=a𝒟 t γ x(ξ),𝒟 t α x(0)=0, where 𝒟 t β ,𝒟 t α ,𝒟 t γ are the standard Riemann-Liouville derivatives with 1<α2,0<β1,0<γ1,0α-γ-1,ξ(0,1) and the constant a is a positive number satisfying aξ 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.
35R11Fractional partial differential equations
35B09Positive solutions of PDE