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Boundedness of Multilinear Caldern–Zygmund Singular Operators on Morrey–Herz Spaces with variable exponents

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Acta Mathematica Sinica,English Series 2014年第7期30卷 1180-1194页

作者： Yan LU Yue Ping ZHU School of Xinglin Nantong University School of Science Nantong University

In this paper, we introduce Morrey-Herz spaces MKq.p（·）α（·）,λ with variable exponents α（·） and p（·）, and prove the boundedness of multilinear Calderdn-Zygmund singular operators on the product of these... 详细信息

关键词： Morrey-Herz spaces variable exponents multilinear Calder6n-Zygmund singular operators

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variable Hardy Spaces on the Heisenberg Group

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Analysis in Theory and Applications 2016年第3期32卷 242-271页

作者： Jingxuan Fang Jiman Zhao School of Mathematical Sciences Key Laboratory of Mathematics and Complex Systems Ministry of Education Beijing Normal University Beijing 100875 China

We consider Hardy spaces with variable exponents defined by grand maximal function on the Heisenberg group. Then we introduce some equivalent characterizations of variable Hardy spaces. By using atomic decomposition and molecular decomposition we get the boundedness of singular integral operators on variable Hardy spaces. We investigate the Littlewood-Paley characterization by virtue of the boundedness of singular integral operators.

关键词： Hardy spaces variable exponents Heisenberg group atomic decomposition Littlewood-Paley characterization.

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STRONGLY NONLINEAR VARIATIONAL PARABOLIC EQUATIONS WITH p(x)-GROWTH

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Acta Mathematica Scientia 2016年第5期36卷 1383-1404页

作者： Elhoussine AZROUL Badr LAHMI Ahmed YOUSSFI Department of Mathematics Faculty of Sciences Dhar El Mahraz University Sidi Mohamed Ben AbdellahLaboratory LAMA University Sidi Mohamed Ben Abdellah National School of Applied Sciences Laboratory of Engineering Systems and Applications

We study the Dirichlet problem associated to strongly nonlinear parabolic equations involving p（x） structure in W;L;（Q）. We prove the existence of weak solutions by applying Galerkin’s approximation method.

关键词： nonlinear parabolic equations existence variable exponents weak solution

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New Class of Kirchhoff Type Equations with Kelvin-Voigt Damping and General Nonlinearity:Local Existence and Blow-up in Solutions

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Journal of Partial Differential Equations 2021年第4期34卷 313-347页

作者： DRIDI Hanni ZENNIR Khaled Laboratory of applied mathematics Badji Mokhtar university.P.O.Box 1223000 AnnabaAlgeria Department of Mathematics College of Sciences and ArtsQassim UniversityAr-RassSaudi Arabia Laboratoire de Mathematiques Appliquees et de Modelisation Universite 8 Mai 1945 Guelma.B.P.401 Guelma 24000 Algerie

In this paper,we consider a class of Kirchhoff equation,in the presence of a Kelvin-Voigt type damping and a source term of general nonlinearity forms.Where the studied equation is given as followsutt-K(Nu(t))[Δ_(p(x))^(u)+Δ_(r(x))^(ut)]=F(x,t,u).Mere,K(Nu(t))is a Kirchhoff function,Δ_(r(x))^(ut)represent a Kelvin-Vbigt strong damp-ing term,and F(x,t,u)is a source term.According to an appropriate assumption,we obtain the local existence of the weak solutions by applying the Galerkin's approximation method.Furthermore,we prove a non-global existence result for certain solutions with negative/positive initial energy.More precisely,our aim is to find a sufficient conditions for p(x)/q(x)/r(x)/F(x/t/u)and the initial data for which the blow-up occurs.

关键词： Galerkin approximation variable exponents Kirchhoff equation blow-up of solutions Kelvin-Voigt damping general nonlinearity

The Eigenvalue Problem for p(x)-Laplacian Equations Involving Robin Boundary Condition

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Journal of Mathematical Research with Applications 2018年第1期38卷 63-76页

作者： Lujuan YU Fengquan LI Fei XU School of Mathematical Sciences Dalian University of Technology

This paper studies the eigenvalue problem for p(x)-Laplacian equations involving Robin boundary condition. We obtain the Euler-Lagrange equation for the minimization of the Rayleigh quotient involving Luxemburg norms in the framework of variable exponent Sobolev space. Using the Ljusternik-Schnirelman principle, for the Robin boundary value problem, we prove the existence of infinitely many eigenvalue sequences and also show that, the smallest eigenvalue exists and is strictly positive, and all eigenfunctions associated with the smallest eigenvalue do not change sign.

关键词： variable exponents eigenvalue Robin boundary condition p(x)-Laplacian equations