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A CLASS OF NONLINEAR BOUNDARY VALUE PROBLEMS FOR THE SECOND-ORDER E_2 CLASS elliptic systems IN GENERAL FORM

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Applied Mathematics and Mechanics(English Edition) 2003年第2期24卷 163-181页

作者：李明忠徐定华 DepartmentofMathematics

A class of nonlinear boundary value problems(BVP) for the second_order E 2 class elliptic systems in general form is discussed. By introducing a kind of transformation,this kind of BVP is reduced to a class of generalized nonlinear Riemann_Hilbert BVP. And then some singular integral operators are introduced to establish the equivalent nonlinear singular integral equations. The solvability is proved under some suitable hypotheses by means of the properties of singular integral operators and the function theoretic methods.

关键词： elliptic systems boundary value problems singular integral equations singular integral operators existence

pde2path – A Matlab Package for Continuation and Bifurcation in 2D elliptic systems

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Numerical Mathematics(Theory,Methods and Applications) 2014年第1期7卷 58-106页

作者： Hannes Uecker Daniel Wetzel Jens D.M.Rademacher Institut für Mathematik Universität Oldenburg26111 OldenburgGermany Universität Bremen Fachbereich MathematikPostfach 33044028359 BremenGermany

pde2path is a free and easy to use Matlab continuation/bifurcation package for elliptic systems of PDEs with arbitrary many components,on general two dimensional domains,and with rather general boundary *** package is based on the FEM of the Matlab pdetoolbox,and is explained by a number of examples,including Bratu’s problem,the Schnakenberg model,Rayleigh-Bénard convection,and von Karman plate *** serve as templates to study new problems,for which the user has to provide,via Matlab function files,a description of the geometry,the boundary conditions,the coefficients of the PDE,and a rough initial guess of a *** basic algorithm is a one parameter arclength-continuation with optional bifurcation detection and *** calculations,error control and mesh-handling,and some elementary timeintegration for the associated parabolic problem are also *** continuation,branch-switching,plotting etc are performed via Matlab command-line function calls guided by the AUTO *** software can be downloaded from ***/*** ker/pde2path,where also an online documentation of the software is provided such that in this paper we focus more on the mathematics and the example systems.

关键词： elliptic systems continuation and bifurcation finite element method

Eigenvalues of elliptic systems for the Mixed Problem in Perturbations of Lipschitz Domains with Nonhomogeneous Neumann Boundary Conditions

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Journal of Partial Differential Equations 2020年第1期33卷 48-63页

作者： MIYAZAKI Kohei TAYLOR Justin L. Department of Mathematics&Statistics Murray State UniversityMurrayKentuckyU.S.A

We study eigenvalues of an elliptic operator with mixed boundary conditions on very general decompositions of the *** impose nonhomogeneous conditions on the part of the boundary where the Neumann term lies in a certain Sobolev or Lp *** work compares the behavior of and gives a relationship between the eigenvalues and eigenfunctions on the unperturbed and perturbed domains,respectively.

关键词： Eigenvalues elliptic systems mixed problem perturbed domains

On Nonlocal elliptic systems of p(x)-Kirchhoff-Type under Neumann Boundary Condition

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Journal of Mathematical Research with Applications 2013年第4期33卷 443-450页

作者： Guowei DAI Xiaoyan LI Department of Mathematics Northwest Normal University

This paper is concerned with the existence of solutions to a class of p(x)-Kirchhofftype systems under Neumann boundary condition. By Ekeland Variational Principle and the theory of the variable exponent Sobolev spaces, we establish conditions ensuring the existence of solutions for the problem. Since the Poincar’e’s inequality does not hold in the space W 1,p(x) (Ω), we shall prove the Poincar’e-Wirtinger’s inequality in a subspace of W 1,p(x) (Ω).

关键词： variational method elliptic systems nonlocal Neumann boundary.

Existence of Positive Solutions to Semilinear elliptic systems Involving Concave and Convex Nonlinearities

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Journal of Physical Science and Application 2015年第1期5卷 71-81页

作者： Mohamed E1 Mokhtar ould El Mokhtar Departement of Mathematics Qassim University BO 6644 Buraidah 51452 Kingdom of Saudi Arabia

In this paper, we studied the combined effect of concave and convex nonlinearities on the number of positive solutions for a semilinear elliptic system. We prove the existence of at least four positive solutions for a semilinear elliptic system involving concave and convex nonlinearities by using the Nehari manifold and the center mass function.

关键词： elliptic systems concave and convex nonlinearities Nehari manifold maximum principle.

EXISTENCE OF TWO POSITIVE SOLUTIONS TO SINGULAR elliptic systems WITH WEIGHTS

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Annals of Differential Equations 2011年第3期27卷 343-351页

作者： Dengfeng Lü(School of Math. and Statistics,Xiaogan University,Xiaogan 432000,Hubei)

In this paper,a class of singular elliptic systems involving weight functions and nonlinear terms are studied. By the fibering method introduced by Pohozaev and the strong maximum principle,the existence of two positi... 详细信息

关键词： elliptic systems positive solution fibering method

Maximum Principle for Nonlinear Cooperative elliptic systems on R^N

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Journal of Partial Differential Equations 2011年第3期24卷 264-280页

作者： LEADI Liamidi MARCOS Aboubacar Institut de Mathematiques et de Sciences Physiques Universite d'Abomey Calavi

We investigate in this work necessary and sufficient conditions for having a Maximum Principle for a cooperative elliptic system on the whole R^N. Moreover, we prove the existence of solutions by an approximation meth... 详细信息

关键词： elliptic systems p-Laplacian operator principal eigenvalues Leray-Schauder fixedpoint approximation method.

Existence Results for a Class of Semilinear elliptic systems

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Journal of Partial Differential Equations 2009年第2期22卷 111-126页

作者： MOUSSAOUI Abdelkrim KHODJA Brahim Department of Biology A. Mira Bejaia University 06000 Bejaia Algeria Department of Mathematics Badji-Mokhtar Annaba University B.P 12 23000 Annaba Algeria

In this paper, we study the existence of nontrivial solutions for the problem{-△u=f（x,u,v）＋h1（x）in Ω -△v=g（x,u,v）＋h2（x）inΩ u=v=0 onδΩwhere Ω is bounded domain in R^N and h1,h2 ∈ L^2 （Ω）. The existence result is obtained by using the Leray-Schauder degree under the following condition on the nonlinearities f and g：{lim s,｜t｜→＋∞f（x,s,t）/s=lim ｜s｜,t→＋∞g（x,s,t）/t=λ＋1 uniformly on Ω, lim -s,｜t｜→＋∞f（x,s,t）/s=lim ｜s｜,-t→＋∞g（x,s,t）/t=λ-,uniformly on Ω,where λ＋,λ-∈（0）∪σ（-△）,σ（-△）denote the spectrum of -△. The cases （i） where λ＋ = λ_ and （ii） where λ＋≠λ_ such that the closed interval with endpoints λ＋,λ_ contains at most one simple eigenvatue of -△ are considered.

关键词： elliptic systems homotopy topological degree

Control of Cauchy System for an elliptic Operator

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Acta Mathematica Sinica,English Series 2009年第11期25卷 1819-1834页

作者： G. MASSENGO MOPHOU O. NAKOULIMA Laboratoire de Mathematiques et Informatique Universite des Antilles et de La Guyane Campus Fouillole 97159 Pointe-a-Pitre GUADELOUPE ( FWI)

The control of a Cauchy system for an elliptic operator seems to be globally an open problem. In this paper, we analyze this problem using a regularization method which consists in viewing a singular problem as a limit of a family of well-posed problems. Following this analysis and assuming that the interior of considered convex is non-empty, we obtain a singular optimality system （S.O.S.） for the considered control problem.

关键词： optimal control optimality conditions elliptic systems