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一类拟线性椭圆方程组非平凡解的存在性 被引量：3

Existence of nontrival solutions for a class of quasilinear elliptic system
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摘要 首先证明了一个抽象的紧性定理,然后借此定理证明了对应于一类拟线性椭圆方程组的泛函在比Boccardo和De.Figueiredo(2002)的条件更弱的条件(文中记为弱类(AR)条件)下满足(C)条件,并利用山路引理证明了这类拟线性椭圆方程组非平凡解的存在性,最后举出两个例子验证了文中所给条件(即弱类(AR)条件)的确比Boccardo和De.Figueiredo(2002)的条件弱. An abstract compactness theorem is proved.Under the condition (called weakened(AR) condition in this paper) weaker than Boccardo and De Figueiredo(2002)condition,by using the above compactness theorem it is proved that the functional corresponding to a class of quasilinear elliptic equations satisfies(C) condition.The existence of nontrival solutions for this elliptic system is proved by means of Mountain-Pass lemma.At last, two examples are presented to illustrate that the weakened(AR) condition is really weaker than Boccardo and De Figueiredo(2002)condition.
作者 章国庆 刘三阳
机构地区 西安电子科技大学应用数学系
出处 《高校应用数学学报（A辑）》 CSCD 北大核心 2004年第3期297-302,共6页 Applied Mathematics A Journal of Chinese Universities(Ser.A)
基金 教育部跨世纪优秀人才基金(2003年)
关键词 抽象紧性定理 弱类(AR)条件 (C)条件 山路引理 abstract compactness theorem weakened(AR) condition (C) condition mountain-pass lemma
分类号 O175.25 [理学—基础数学]
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参考文献5

  • 1Ambrosetti A,Rabinowitz P H.Dual variational methods in critical points theory and applications[J].Journal of Functional Analysis,1973,14:349-381.
  • 2Costa G,Magalhaes C A.Existence results for perturbations of the P- Laplacian[J].Nonlinear Analysis TMA,1995,25:409-418.
  • 3Bartolo P,Benci V,Fortunato D.Abstract critical point theorems and applications to some nonlinear problems with strong resonance at infinity[J].Nonlinear Analysis TMA,1983,7:981-1012.
  • 4Boccardo L,Figueiredo D G De.Some remarks on a system of quasilinear elliptic equations[J].Nonlinear Differential Equations and Applications,2002,9:309-323.
  • 5Rudin W.Real and Complex Analysis[M].Second Edition,New York:McGraw- Hill,1974.

同被引文献19

  • 1RABINOWITZ P H. On a class of nonlinear Schrodinger equations[J]. ZAMP, 1992,43 : 270 - 291.
  • 2COSTA D G,MAGALHAES C A. A variational approach m noncooperative elliptic systems[J]. Nonlinear Anal, 1995,25 : 699 - 715.
  • 3BOCCARDO L,de FIGUEIREDO D G. Some remarks on a system of quasilinear elliptic equations[J]. NoDEA, 2002,9: 309 - 323.
  • 4I COFFMAN C V. A minimum-maximum principle for I class of nonlinear integral equations [J]. J. AnalI I Math. ,1969,22:391 - 419.
  • 5WILLEM M. Minmax theorems[M]. Boston: Birkhauser, 1996.
  • 6BREZIS H,NIRENBERG L. Remarks on finding critical points[J]. Commun. Pure. Appl. Math., 1991, 44:939 - 963.
  • 7Boccardo L,de Figueiredo D G. Some remarks on a system of quasilinear elliptic equations[J]. Nonlinear Differential Equations Appl. , 2002,9 : 309-323.
  • 8Ambrosetti A,Rabinowitz P H. Dual variational methods in critical points theory and applieations[J]. Journal of Functional Analysis, 1973,14 : 349-381.
  • 9Willem M. Minmax Theorems[M]. Boston: Birkhauser, 1996.
  • 10Lions P L. The concentration-compactness principle in the calculus of variations[J]. Rev. Mat. Ibero Americana ,1985,1 (1) : 145-201.

引证文献3

二级引证文献1

高校应用数学学报（A辑）
2004年 第3期

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