Boundary value problem with fractional p-Laplacian operator

Boundary value problem with fractional p-Laplacian operator

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 sa...

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Bibliographic Details
Published in:Advances in nonlinear analysis Vol. 5; no. 2; pp. 133 - 146
Main Author: Torres Ledesma César
Format: Journal Article
Language:English
Published: De Gruyter 01-05-2016
Subjects:
26a33
58e05
65l10
boundary value problem
fractional calculus
mixed fractional derivatives
mountain pass theorem
p-laplacian operator
Online Access:Get full text
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Summary: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.
ISSN:2191-9496
2191-950X
DOI:10.1515/anona-2015-0076