We study integral vectorial functionals F(u;) ? Z f(x; u(x); Du(x))dx where f satisses quasi-convexity assumption and its growth is controlled in term of N-functions. We obtain semicontinuity results in the weak * topology of Orlicz-Sobolev spaces.

This paper is concerned with the multiplicity of nontrivial solutions in an Orlicz-Sobolev space for a nonlocal problem with critical growth, involving N-functions and theory of locally Lispchitz continuous functionals. More precisely, in this paper, we study a result of multiplicity to the following multivalued elliptic problem:

Abstract In the present paper we study perturbed sampling Kantorovich operators in general context of modular spaces. After proving a convergence result for continuous functions with compact support, by using both inequality and density approach, establish main these operators. Further, show several instances spaces which results can be applied. particular, some applications Musielak–Orlicz Orl...

We provide necessary and sufficient conditions for the space of smooth functions with compact supports $$C^\infty _c(\Omega )$$ to be dense in Musielak–Orlicz spaces $$L^\Phi (\Omega where $$\Omega $$ is an open subset $${\mathbb {R}}^d$$ . In particular, we prove that if $$\Phi satisfies condition $$\Delta _2$$ , closure )\cap L^\Phi equal only measure singular points zero. This extends earlie...

A necessary and sufficient condition for fractional Orlicz–Sobolev spaces to be continuously embedded into L∞(Rn) is exhibited. Under the same assumption, any function from relevant fractional-order shown continuous. Improvements of this result are also offered. They provide optimal Orlicz target space, rearrangement-invariant space in embedding question. These results complement those already ...

Let M be a non-degenerate Orlicz function such that there exist ǫ > 0 and 0 < s < 1 with ∑ ∞ i=1 M(ǫs)/M(s) < ∞. It is shown that the Orlicz sequence space hM is isomorphic to a subspace of C(ω). It is also shown that for any non-degenerate Orlicz function M , hM does not embed into C(α) for any α < ω .

A Schauder basis (xn) of a Banach space X is said to be lower [upper] semi-homogeneous if every normalized block basic sequence of (xn) dominates [is dominated by] the basis. We show that the unit vector basis of a separable Orlicz sequence space `M , with M(1) = 1 is lower [upper] semihomogeneous if and only if M fulfils some kind of super[sub]-multiplicative inequality on the interval[0, 1]. ...

An Orlicz function ~0 is a real-valued function defined as [0, ~o) satisfying the condition (a) ~0 is non-decreasing (b) (p(0)=0 and ~o is continuous at 0 and (c) (o is not identically zero. In addition ~o satisfies the A2-condition at ~o provided for some C and x (1.0.1) ~0(2x) <_c q , ( x ) x >x or equivalently, for some C (1.0.2) q~(Zx) ~ C( (p (x )+ l ) 0 <_x <o~. I f ~0 satisfies the A.,-c...