Weak and viscosity solutions for non-homogeneous fractional equations in Orlicz spaces

Multiple solutions for Kirchhoff elliptic equations in Orlicz-Sobolev spaces

Fractional Integration in Orlicz Spaces

Fractional integration and convolution results are given for Orlicz spaces using an inequality earlier developed for Aa(X~) spaces which generalize Lorentz L(p,q) spaces. The extension problem for convolution operators encountered previously by other authors is almost entirely avoided.

Weak and Viscosity Solutions of the Fractional Laplace Equation

Aim of this paper is to show that weak solutions of the following fractional Laplacian equation { (−∆)su = f in Ω u = g in Rn \ Ω are also continuous solutions (up to the boundary) of this problem in the viscosity sense. Here s ∈ (0, 1) is a fixed parameter, Ω is a bounded, open subset of Rn (n > 1) with C2-boundary, and (−∆)s is the fractional Laplacian operator, that may be defined as (−∆)u(x...

Weak Solutions for Nonlinear Fractional Differential Equations with Integral Boundary Conditions in Banach Spaces

The aim of this paper is to investigate a class of boundary value problems for fractional differential equations involving nonlinear integral conditions. The main tool used in our considerations is the technique associated with measures of weak noncompactness.

Semi-homogeneous Bases in Orlicz Sequence Spaces

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]. ...