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Existence of positive solutions for a fractional boundary value problem with lower-order fractional derivative dependence on the half-line

Amina BoucennaToufik Moussaoui — 2014

Discussiones Mathematicae, Differential Inclusions, Control and Optimization

The aim of this paper is to study the existence of solutions to a boundary value problem associated to a nonlinear fractional differential equation where the nonlinear term depends on a fractional derivative of lower order posed on the half-line. An appropriate compactness criterion and suitable Banach spaces are used and so a fixed point theorem is applied to obtain fixed points which are solutions of our problem.

Existence Results for a Fractional Boundary Value Problem via Critical Point Theory

A. BoucennaToufik Moussaoui — 2015

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica

In this paper, we consider the following boundary value problem D T - α ( D 0 + α ( D T - α ( D 0 + α u ( t ) ) ) ) = f ( t , u ( t ) ) , t [ 0 , T ] , u ( 0 ) = u ( T ) = 0 D T - α ( D 0 + α u ( 0 ) ) = D T - α ( D 0 + α u ( T ) ) = 0 , where 0 < α 1 and f : [ 0 , T ] × is a continuous function, D 0 + α , D T - α are respectively the left and right fractional Riemann–Liouville derivatives and we prove the existence of at least one solution for this problem.

Existence and multiplicity of solutions for a fractional p -Laplacian problem of Kirchhoff type via Krasnoselskii’s genus

Ghania BenhamidaToufik Moussaoui — 2018

Mathematica Bohemica

We use the genus theory to prove the existence and multiplicity of solutions for the fractional p -Kirchhoff problem - M Q | u ( x ) - u ( y ) | p | x - y | N + p s d x d y p - 1 ( - Δ ) p s u = λ h ( x , u ) in Ω , u = 0 on N Ω , where Ω is an open bounded smooth domain of N , p > 1 , N > p s with s ( 0 , 1 ) fixed, Q = 2 N ( C Ω × C Ω ) , λ > 0 is a numerical parameter, M and h are continuous functions.

Existence and multiplicity of solutions for a p ( x ) -Kirchhoff type problem via variational techniques

A. MokhtariToufik MoussaouiD. O’Regan — 2015

Archivum Mathematicum

This paper discusses the existence and multiplicity of solutions for a class of p ( x ) -Kirchhoff type problems with Dirichlet boundary data of the following form - a + b Ω 1 p ( x ) | u | p ( x ) d x div ( | u | p ( x ) - 2 u ) = f ( x , u ) , i n Ω u = 0 o n Ω , where Ω is a smooth open subset of N and p C ( Ω ¯ ) with N < p - = inf x Ω p ( x ) p + = sup x Ω p ( x ) < + , a , b are positive constants and f : Ω ¯ × is a continuous function. The proof is based on critical point theory and variable exponent Sobolev space theory.

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