Abstract
Abstract The aim of this paper is to obtain the existence of solution for the fractional p-Laplacian Dirichlet problem with mixed derivatives t D T α(|0 D t α u(t)| p-2 0 D t α u(t)) = f(t,u(t)), t ∈ [0,T], u(0) = u(T) = 0, where 1/p < α < 1, 1 < p < ∞ and f : [0,T] × ℝ → ℝ is a Carathéodory function which satisfies some growth conditions. We obtain the existence of nontrivial solutions by using the direct method in variational methods and mountain pass theorem.
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