The aim of this paper is to obtain the existence of solution for the fractional p-Laplacian Dirichlet problem with mixed derivatives
tDTα(|0Dtαu(t)|p-20Dtαu(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.
Our new journal Advances in Nonlinear Analysis aims to publish very selected research contributions devoted to nonlinear problems coming from different areas, with particular reference to those introducing new techniques capable of solving a wide range of problems.