Anisotropic and Orthomorphisms on Non-Banach F-Lattices with Gosses Approximation Theorems on Musielak-Orlicz-Sobolev Spaces

Abstract

We show a sharp embedding theorem, some existence results on periodic solutions of Euler-Lagrange equations and anisotropic in Orlicz-Sobolev spaces setting and of vector valued functions. The centre of a vector lattice with the problem of central orthomorphisms in a class of F-lattices and some monotonicity properties in central s-normed and F-normed lattices are considered. We deal with the sequence space and Orthomorphisms on non-Banach F-lattices containing a copy of the Euclidean space with applications to Musielak-Orlicz spaces. We show a guide to nonlinear differential equations and some approximation results in Musielak-Orlicz spaces. We introduce some approximation properties and Gossez approximation theorems in Musielak-Orlicz-Sobolev spaces.