Positive Solution for the Integral and Infinite Point Boundary Value Problem for Fractional-Order Differential Equation Involving a Generalized ϕ-Laplacian Operator

Abstract EN

In this paper, we establish the existence of nontrivial positive solution to the following integral-infinite point boundary-value problem involving ϕ-Laplacian operator D0+αϕx,D0+βux+fx,ux=0,x∈0,1,D0+σu0=D0+βu0=0,u1=∫01 gtutdt+∑n=1n=+∞ αnuηn, where ϕ:0,1×R→R is a continuous function and D0+p is the Riemann-Liouville derivative for p∈α,β,σ.

By using some properties of fixed point index, we obtain the existence results and give an example at last.