The Nehari Manifold for a Class of Singular $\psi$-Riemann-Liouville Fractional with $p$-Laplacian Operator Differential Equations

Abstract

Using Nehari manifold method combined with fibring maps, we show the existence of nontrivial, weak, positive solutions of the nonlinear $\psi$-Riemann-Liouville fractional boundary value problem involving the $p$-Laplacian operator, given by 

where $λ>0, 0<\gamma<1< p$ and $\frac{1}{p}<\alpha≤1,$ $g∈C([0,T])$ and $f ∈C^1 ([0,T]×\mathbb{R},\mathbb{R}).$ A useful examples are presented in order to illustrate the validity of our main results.