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Existence of Explosive Solutions for a Class of nonlinear elliptic equations

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Journal of Donghua University(English Edition) 2008年第6期25卷 676-679页

作者：彭亚红彭小珍 Department of Applied Mathematics Donghua University

By the subsuper solutions method, the explosive supersolutions and explosive subsol utions are obtained and the exsistence of explosive solutions is proved on a bounded domain for a class of nonlinear elliptic ***, th... 详细信息

关键词： nonlinear elliptic equations explosive supersolutions explosive subsolutions

SOME nonlinear elliptic equations HAVE ONLY CONSTANT SOLUTIONS

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Journal of Partial Differential equations 2006年第3期19卷 208-217页

作者： Haim Brezis Li Yanyan Laboratoire J.-L. Lions Université P. ET M. Curie B.C. 187 4 PL. Jussieu 75252 Paris Cedex 05 France Rutgers University Dept. of Math. Hill Center Busch Campus 110 Frelinghuysen RD Piscataway NJ 08854 USA Rutgers University Dept. of Math. Hill Center Busch Campus 110 Frelinghuysen RD Piscataway NJ 08854 USA

We study some nonlinear elliptic equations on compact Riemannian manifolds. Our main concern is to find conditions which imply that such equations admit only constant solutions.

关键词： nonlinear elliptic equations constant solutions.

SOME BOUNDARY VALUE PROBLEMS FOR nonlinear DEGENERATE elliptic equations OF SECOND ORDER

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Acta Mathematica Scientia 2007年第3期27卷 663-672页

作者：闻国椿 School of Mathematical Sciences Peking University

The present article deals with some boundary value problems for nonlinear elliptic equations with degenerate rank 0 including the oblique derivative problem. Firstly the formulation and estimates of solutions of the oblique derivative problem are given, and then by the above estimates and the method of parameter extension, the existence of solutions of the above problem is proved. In this article, the complex analytic method is used, namely the corresponding problem for degenerate elliptic complex equations of first order is firstly discussed, afterwards the above problem for the degenerate elliptic equations of second order is solved.

关键词： Boundary value problems nonlinear elliptic equations parabolic degeneracy

L∞-ESTIMATES OF MIXED FINITE ELEMENT METHODS FOR GENERAL nonlinear OPTIMAL CONTROL PROBLEMS

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Journal of Systems Science & Complexity 2012年第1期25卷 105-120页

作者： Yanping CHEN Zuliang LU School of Mathematical Sciences South China Normal University School of Mathematics and Statistics Chongqing Three Gorges University College of Civil Engineering and Mechanics Xiangtan University

This paper investigates L∞--estimates for the general optimal control problems governed by two-dimensional nonlinear elliptic equations with pointwise control constraints using mixed finite element methods. The state and the co-state are approximated by the lowest order Raviart-Thomas mixed finite element spaces and the control is approximated by piecewise constant functions. The authors derive L∞--estimates for the mixed finite element approximation of nonlinear optimal control problems. Finally, the numerical examples are given.

关键词： L∞--error estimates mixed finite element methods nonlinear elliptic equations optimalcontrol problems pointwise control constraints.

Regularity of Weak Solutions of nonlinear equations with Discontinuous Coefficients

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Acta Mathematica Sinica,English Series 2005年第4期21卷 705-714页

作者： Qi Kang RAN Departtnent of Applied Mathematics Shanghai University of Finance and Economics Shanghai 200433 P. R. China

In this paper, we prove that the weak solutions u∈Wloc^1, p （Ω）（1 〈p〈∞） of the following equation with vanishing mean oscillation coefficients A（x）： -div[（A（x）△↓u·△↓u）p-2/2 A（x）△↓u＋│F（x）│^p-2 F（x）]=B（x, u, △↓u）, belong to Wloc^1, q （Ω）（A↓q∈（p, ∞）, provided F ∈ Lloc^q（Ω） and B（x, u, h） satisfies proper growth conditions where Ω ∪→R^N（N≥2） is a bounded open set, A（x）=（A^ij（x）） N×N is a symmetric matrix function.

关键词： nonlinear elliptic equations Local Regularity Calderon-Zygmund decomposition VMO space Local weak L^p(Ω) space

The Solutions of the Coupled Einstein-Maxwell equations and Dilaton equations

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Acta Mathematicae Applicatae Sinica 2018年第3期34卷 485-492页

作者： Rui-feng ZHANG Ya GU Institute of Contemporary Mathematics Henan University Kaifeng 475004 China School of Mathematics and Statistics Henan University Kaifeng 475004 China

In this paper, we consider extremely charged static perfect fluid distributions with a dilaton field in the framework of general relativity. By using calculus of variations, we establish the existence theorem for the solutions of this important gravitational system. We show that there is a continuous family of smooth solutions realizing asymptotically flat space metrics.

关键词： nonlinear elliptic equations the variational method the asymptotic estimates.

elliptic equations with Degenerate Coercivity： Gradient Regularity

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Acta Mathematica Sinica,English Series 2003年第2期19卷 349-370页

作者： DanielaGIACHETTI MariaMichaelaPORZIO DipartimentodiMetodieModelliMatematiciperleScienzeApplicate UniversitàdegliStudidiRoma'LaSapienza'viaA.Scfarpa1600161RomaItaly FacoltádiScienzeMatematiche FisicheeNaturaliUniversitádegliStudidelSannioviaPort'Arsa1182100BeneventoItaly

In this paper, we prove higher integrability results for the gradient of the solutions of some elliptic equations with degenerate coercivity whose prototype is$ - {\rm div}\left( {a\left( {x,u} \right)Du} \right) = f$ in $D^' \left( \Omega \right),\,\,f \in L^r \left( \Omega \right),\,\,r > 1$where for example, a(x,u)=(1+|u|)^m/ with / ] (0,1). We study the same problem for minima of functionals closely related to the previous equation.

关键词： Regularity of solutions nonlinear elliptic equations Functionals of calculus of variations

Maximum Principles for a Class of nonlinear elliptic Boundary Value Problems

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Acta Mathematicae Applicatae Sinica 2005年第3期21卷 373-380页

作者： Jun-tang Ding Sheng-jia Li Jiang-hao Hao School of Mathematical Sciences Shanxi University Taiyuan 030006 China

The Hopf＇s maximum principles are utilized to obtain maximum principles for functions defined on solutions of nonlinear elliptic equations in divergence form （g（u）u,i）,i ＋f（x,u,q）=0（q=｜△↓u｜^2）, subject T... 详细信息

关键词： nonlinear elliptic equations maximum principles bounds of gradient

Deformation Argument under PSP Condition and Applications

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Analysis in Theory and Applications 2021年第2期37卷 191-208页

作者： Silvia Cingolani Kazunaga Tanaka Dipartimento di Matematica Universit`a degli Studi di Bari Aldo MoroVia E.Orabona 470125 BariItaly Department of Mathematics School of Science and EngineeringWaseda University3-4-1 OhkuboShijuku-kuTokyo 169-8555Japan

In this paper we introduce a new deformation argument,in which C^(0)-group action and a new ty pe of Palais Smale condition PSP play important *** type of deformation results are studied in[17,21]and has many different applications[10,11,17,21]et *** it can be applied to nonlinear scalar field *** give a survey in an abstract functional *** also present another application to nonlinear elliptic problems in strip-like *** conditions related to[5,6],we show the existence of infinitely many *** ex tends the results in[8].

关键词： Deformation theory nonlinear elliptic equations radially symmetric solutions striplike domains Pohozaev functional