Related papers: Perturbation Method in Musielak-Orlicz Sequence Sp…

In this paper we introduce a new logarithmic double phase type operator of the form\begin{align*}\mathcal{G}u:=-\operatorname{div}\left(|\nabla u|^{p(x)-2}\nabla u+\mu(x)\left[\log(e+|\nabla u|)+\frac{|\nabla u|}{q(x)(e+|\nabla…

In this paper, we study spaceability of subsets of generalized Orlicz and Lebesgue spaces associated to Banach function space. Also, we give some sufficient conditions for spaceability of subsets of a general Banach space which improves an…

Our studies are directed to the existence of weak solutions to a parabolic problem containing a multi-valued term. The problem is formulated in the language of maximal monotone graphs. We assume that the growth and coercivity conditions of…

In this paper, we are concerned with some qualitative properties of the new fractional Musielak-Sobolev spaces $W^sL_{\varPhi_{x,y}}$ such that the generalized Poincar\'e type inequality and some continuous and compact embedding theorems of…

We consider a stochastic parabolic partial differential equation with Dirichlet boundary conditions, multiplicative stochastic noise, and a monotone parabolic operator A. The growth and coercivity of A is controlled by a general N-function…

We introduce a new class of Hardy spaces $H^{\varphi(\cdot,\cdot)}(\mathbb R^n)$, called Hardy spaces of Musielak-Orlicz type, which generalize the Hardy-Orlicz spaces of Janson and the weighted Hardy spaces of Garc\'ia-Cuerva, Str\"omberg,…

We introduce a framework based on Rockafellar's perturbation theory to analyze and solve general nonsmooth convex minimization and monotone inclusion problems involving nonlinearly composed functions as well as linear compositions. Such…

A plethora of spaces in Functional Analysis (Braun-Meise-Taylor and Carleman ultradifferentiable and ultraholomorphic classes; Orlicz, Besov, Lipschitz, Lebesque spaces, to cite the main ones) are defined by means of a weighted structure,…

The objective of this paper is to introduce and study a complicated nonlinear system, called coupled variational-hemivariational inequalities, which is described by a highly nonlinear coupled system of inequalities on Banach spaces. We…

We show that the weighted Bergman-Orlicz space $A\_{\alpha}^{\psi}$ coincides with some weighted Banach space of holomorphic functions if and only if the Orlicz function $\psi$ satisfies the so-called $\Delta^{2}$--condition. In addition we…

In this work the Melnikov method for perturbed Hamiltonian wave equations is considered in order to determine possible chaotic behaviour in the systems. The backbone of the analysis is the multi-symplectic formulation of the unperturbed PDE…

We develop an operator-theoretical method for the analysis on well posedness of partial differential equations that can be modeled in the form \begin{equation*} \left\{ \begin{array}{rll} \Delta^{\alpha} u(n) &= Au(n+2) + f(n,u(n)), \quad n…

We study unbounded weak supersolutions of elliptic partial differential equations with generalized Orlicz (Musielak--Orlicz) growth. We show that they satisfy the weak Harnack inequality with optimal exponent provided that they belong to a…

Let $X$ be a real Banach space with its dual $X^*$ and $G$ be a nonempty, bounded and open subset of $X$ with $0\in G$. Let $T: X\supset D(T)\to 2^{X}$ be an $m$-accretive operator with $0\in D(T)$ and $0\in T(0)$, and let $C$ be a compact…

Concentration compactness method is a powerful techniques for establishing existence of minimizers for inequalities and of critical points of functionals in general. The paper gives a functional-analytic formulation for the method in Banach…

We prove in this article that every Borelian measure, for example, the distribution of a random variable, in separable Banach space has a support which is compact embedded Banach subspace; and prove that if the norm of the random variable…

This paper develops the necessary ingredients for the variational approach of initial boundary-value problems of parabolic partial differential equations on a fixed spatial domain containing evolving subdomains. In particular, we introduce…

We consider the space $\mathcal{D}'^r_L(M;E)$ of distributional sections of the smooth complex vector bundle $E\rightarrow M$ whose Sobolev wave front set of order $r\in\mathbb{R}$ lies in the closed conic subset $L$ of $T^*M\backslash0$.…

Poincar\'{e}-Sobolev-type inequalities involving rearrangement-invariant norms on the entire $\mathbb{R}^n$ are provided. Namely, inequalities of the type $\|u-P\|_{Y(\mathbb{R}^n)}\leq C\|\nabla^m u\|_{X(\mathbb{R}^n)}$, where $X$ and $Y$…

We prove existence of renormalized solutions to general nonlinear elliptic equation in Musielak-Orlicz space avoiding growth restrictions. Namely, we consider \begin{equation*} -{\rm div} A(x,\nabla u)= f\in L^1(\Omega), \end{equation*} on…