Research on Sturm–Liouville boundary value problems of fractional p-Laplacian equation.

In this work we investigate the following fractional p-Laplacian differential equation with Sturm–Liouville boundary value conditions: { D T α t (1 (h (t)) p − 2 ϕ p (h (t) 0 C D t α u (t))) + a (t) ϕ p (u (t)) = λ f (t , u (t)) , a.e. t ∈ [ 0 , T ] , α 1 ϕ p (u (0)) − α 2 t D T α − 1 (ϕ p (0 C D t α u (0))) = 0 , β 1 ϕ p (u (T)) + β 2 t D T α − 1 (ϕ p (0 C D t α u (T))) = 0 , where D t α 0 C , D T α t are the left Caputo and right Riemann–Liouville fractional derivatives of order α ∈ (1 2 , 1 ] , respectively. By using variational methods and critical point theory, some new results on the multiplicity of solutions are obtained. [ABSTRACT FROM AUTHOR]