Electronic Journal of Differential Equations, 
Vol. 2021 (2021), No. 26, pp. 1-28.

Title: Continuous imbedding in Musielak spaces with an application to anisotropic nonlinear 
       Neumann problems
       
Authors: Ahmed Youssfi (Univ. Sidi Mohamed Ben Abdellah, Fez, Morocco)
         Mohamed Mahmoud Ould Khatri (Univ. Sidi Mohamed Ben Abdellah, Fez, Morocco)

Abstract:
 We prove a continuous embedding that allows us to obtain a boundary trace imbedding
 result for anisotropic Musielak-Orlicz spaces, which we then apply to obtain an
 existence result for Neumann problems with nonlinearities on the boundary associated
 to some anisotropic nonlinear elliptic equations in Musielak-Orlicz spaces constructed
 from Musielak-Orlicz functions on which and on their conjugates we do not assume the
 &Delta;<sub>2</sub>-condition. The uniqueness of weak solutions is also studied.

Submitted April 12, 2019. Published April 05, 2021.
Math Subject Classifications: 46E35, 35J20, 35J25, 35B38, 35D30.
Key Words: Musielak-Orlicz space; imbedding; boundary trace imbedding;
           weak solution; minimizer.