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Some approximation results in Musielak-Orlicz spaces

Ahmed YoussfiYoussef Ahmida — 2020

Czechoslovak Mathematical Journal

We prove the continuity in norm of the translation operator in the Musielak-Orlicz L M spaces. An application to the convergence in norm of approximate identities is given, whereby we prove density results of the smooth functions in L M , in both the modular and norm topologies. These density results are then applied to obtain basic topological properties.

Existence results for a class of nonlinear parabolic equations with two lower order terms

Ahmed AberqiJaouad BennounaM. HammoumiMounir MekkourAhmed Youssfi — 2014

Applicationes Mathematicae

We investigate the existence of renormalized solutions for some nonlinear parabolic problems associated to equations of the form ⎧ ( e β u - 1 ) / t - d i v ( | u | p - 2 u ) + d i v ( c ( x , t ) | u | s - 1 u ) + b ( x , t ) | u | r = f in Q = Ω×(0,T), ⎨ u(x,t) = 0 on ∂Ω ×(0,T), ⎩ ( e β u - 1 ) ( x , 0 ) = ( e β u - 1 ) ( x ) in Ω. with s = (N+2)/(N+p) (p-1), c ( x , t ) ( L τ ( Q T ) ) N , τ = (N+p)/(p-1), r = (N(p-1) + p)/(N+2), b ( x , t ) L N + 2 , 1 ( Q T ) and f ∈ L¹(Q).

Existence of solutions for some quasilinear p ( x ) -elliptic problem with Hardy potential

Elhoussine AzroulMohammed BouzianiHassane HjiajAhmed Youssfi — 2019

Mathematica Bohemica

We consider the anisotropic quasilinear elliptic Dirichlet problem - i = 1 N D i a i ( x , u , u ) + | u | s ( x ) - 1 u = f + λ | u | p 0 ( x ) - 2 u | x | p 0 ( x ) in Ω , u = 0 on Ω , where Ω is an open bounded subset of N containing the origin. We show the existence of entropy solution for this equation where the data f is assumed to be in L 1 ( Ω ) and λ is a positive constant.

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