<abstract xmlns="http://www.w3.org/1999/xhtml"> Some distributional properties of the symmetric arcsine distribution on (−1, 1) is presented. Based on the distributional properties, several characterizations of the arcsine distribution are given.</abstract>

Some characterizations of Arcsine distribution

<abstract xmlns="http://www.w3.org/1999/xhtml"> This paper is devoted to the study of the following fourth order parabolic equation ∂tu + ∂x4u = f in the non-necessarily rectangular domain Q ={(t,x) ∈ℝ2 : 0 &lt; t &lt; T, ϕ1(t) &lt; x &lt; ϕ2(t)}. The equation is subject to mixed type conditions ∂xu = ∂x3u + βu = 0, on the lateral boundary of Q. The right-hand side term f of the equation lies in Lω2 (Q) the space of square-integrable functions on Q with the measure ωdtdx. Our aim is to find sufficient conditions on the coefficient β and on the functions ϕi,i = 1, 2 and on the weight ω such that the solution of this equation belongs to the anisotropic Sobolev space Hω1,4 (Q) = {u ∈ Lω2 (Q) : ∂tu, ∂xju ∈ Lω2 (Q) , j = 1, 2, 3, 4}.The analysis is performed by using the domain decomposition method. </abstract>

On a Fourth Order Parabolic Equation with Mixed Type Boundary Conditions in a Nonrectangular Domain

<abstract xmlns="http://www.w3.org/1999/xhtml"> In this article we study the property (gab) for a bounded linear operator T 2 L(X) on a Banach space X which is a stronger variant of Browder’s theorem. We shall give several characterizations of property (gab). These characterizations are obtained by using typical tools from local spectral theory. We also show that property (gab) holds for large classes of operators and prove the stability of property (gab) under some commuting perturbations.</abstract>

Property (gab) through localized SVEP

<abstract xmlns="http://www.w3.org/1999/xhtml"> In this paper we prove existence results for distributional solutions of nonlinear elliptic systems with a measure data. The functional setting involves Lebesgue-Sobolev spaces as well as weak Lebesgue (Marcinkiewicz) spaces with variable exponents W01,p(·)(Ω) and Mp(·)(Ω) respectively. </abstract>

Institut de Mathématiques de Bordeaux UMR CNRS 5251, Université Victor Segalen Bordeaux 2, F-33076 Bordeaux Cedex,

Laboratoire des EDPNL, ENS-Kouba, Department of Mathematics and Informatics, Faculty of Sciences, Univ of Benyoucef Benkhadda, 2 rue Didouche Mourad, Algiers,

Nonlinear elliptic systems with variable exponents and measure data

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Moroccan Journal of Pure and Applied Analysis

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Moroccan Journal of Pure and Applied Analysis

Volume 1 (2015): Issue 2 (December 2015)

Research Article

Some characterizations of Arcsine distribution

On a Fourth Order Parabolic Equation with Mixed Type Boundary Conditions in a Nonrectangular Domain

Property (gab) through localized SVEP

Nonlinear elliptic systems with variable exponents and measure data

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