一类拟线性椭圆型方程边值问题的稳定性

胡业新

数学学报 ›› 2014, Vol. 57 ›› Issue (6) : 1181-1190.

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数学学报 ›› 2014, Vol. 57 ›› Issue (6) : 1181-1190. DOI: 10.12386/A2014sxxb0108
论文

一类拟线性椭圆型方程边值问题的稳定性

    胡业新
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Stability of Solution for a Class of Quasilinear Elliptic Boundary Problems

    Ye Xin HU
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文章历史 +

摘要

在一定条件下证明了一类拟线性椭圆型方程边值问题W1,p(Ω)∩L∞(Ω) 解的存在唯一性,对p≥2及1<p≤2两种情形分别在集合收敛与点收敛意义下得到了此类解边值的稳定性.

Abstract

We prove that the existence and uniqueness of the solution in the space W1,p(Ω)∩L∞(Ω) for a class of quasi-linear elliptic equations under some conditions.The stability of this kind of weak solutions with respect to Dirichlet boundary data is given in the sense of set convergence for the case p≥2 and in the sense of point convergence for the case 1< p ≤ 2.

关键词

椭圆边值问题 / 拓扑度方法 / 存在唯一性 / 稳定性

Key words

elliptic boundary value problem / topological degree methods / existence and uniqueness / stability

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胡业新. 一类拟线性椭圆型方程边值问题的稳定性. 数学学报, 2014, 57(6): 1181-1190 https://doi.org/10.12386/A2014sxxb0108
Ye Xin HU. Stability of Solution for a Class of Quasilinear Elliptic Boundary Problems. Acta Mathematica Sinica, Chinese Series, 2014, 57(6): 1181-1190 https://doi.org/10.12386/A2014sxxb0108

参考文献

[1] Adams R.A., Sobolev Space, Academic Press, New York, 1975.

[2] Aubin J.P., Frankowska H., Set-Valued Analysis, Birkhauser, Boston, 1990.

[3] Bors D., Walczak S., Nonlinear systems with variable boundary data, Nonlinear Anal.TMA, 2003, 52. 1347-1364.

[4] Drábek P., Kufner A., Nicolosi F., Quasilinear Elliptic Equations with Degenerations and Singularities, de Gruyter Series in Nonlinear Analysis and Applications, Vol.5, Berlin, New York, 1997.

[5] Hu Y.X., Stabilty of weak solutions of a class of non-variational quasi-linear elliptic systems with respect to boundary data, Acta.Math.Sinica, Chinese Series, 2009, 52(1): 117-124.

[6] Peral I., Multiplicity of solutions for the p-Laplacian, Lecture Notes at the Second School on Nonlinear Functional Analysis and Applications to Differential Equations at ICTP of Trieste (April 21-May 9, 1997).

[7] Skrypnik I.V., Methods of Analysis of Nonlinear Elliptic Boundary Value Problems, Translations of Mathematical Monographs, Vol.139, American Mathematical Society, Providence, RI, 1994.

[8] Szulkin A., Willem M., Eigenvalue problems with indefinite weight, Studia.Math., 1999, 135: 191-201.

[9] Willem M., Analysis Harmonique Réelle, Hermann, Paris, 1995.

[10] Willem M., Minimax Theorems, Birkhäuser, Boston, 1996.

基金

国家自然科学基金资助项目(10271077);上海财经大学基础科研业务项目资助

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