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Sobolev临界增长椭圆方程注 被引量：1

Note on Elliptic Equations Involving the Criticial Sobolev Growth
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摘要 利用空间H10(Ω)的正交分解和极小值原理给出了具临界指数2*的椭圆方程-Δu=λ1u-|u|2*-2u+g(x,u)+h(x)1解的存在性定理,这里次临界项g(x,u)关于u是非线性的,λ1为算子-Δ在H10(Ω)中最小特征值.特别当h≡0时,本文还获得了非零解的存在性结论. In this paper, existence theorems of solution for a class of semilinear elliptic equations -△u=λ1u-｜u｜^2＊-2u＋g（x, u）＋h（x）, involving the critical Sobolev exponent 2^＊ and the first eigenvalue λ1, has been given by ways of the least action principle and the orthogonal resolution on the Sobolev space H0^1 （Ω）, where g is the subcritical item to be given. Moreover, a non-zero solution has been obtained in the case of h≡0.
作者 饶若峰
机构地区 宜宾学院数学系
出处 《大学数学》 北大核心 2006年第5期41-44,共4页 College Mathematics
基金 国家自然科学基金资助项目(10071048) 宜宾学院自然科学(青年)基金资助项目(2006001102)
关键词 半线性椭圆方程 SOBOLEV临界指数 DIRICHLET问题 特征值 极小值原理 semilinear elliptic equation the critial Sobolev exponent Dirichlet question the eigenvalue the least action principle
分类号 O175.25 [理学—基础数学]
  • 相关文献

参考文献6

  • 1Capozzi A,Fortunato D,Palmieri G.An Existence Result for Nonlinear Elliptic problems involving Critical Sobolev Exponent[J].Ann.Inst.H.Poincare,1985,2:463-470.
  • 2Ambrosetti A.Struwe M.A Note on the Problem -Δu=λu+u|u|^2*-2[J].Manusc.Math,1986,54:373-379.
  • 3饶若峰.涉及第一特征值和临界指数的一类椭圆方程[J].数学进展,2004,33(6):703-711. 被引量：9
  • 4Tang Chunlei,Gao Qiju.Elliptic Resonant Problems at Higher Eigenvalues with an Unbounded Nonlinear Term[J].Academic Press,1998,0022-0396.
  • 5Mawhin J and Willem M.Critical Point Theory and Hamiltonian Systems[M].New York:Springer-Verlag,1989.
  • 6Zhu Xiping.Non-Trivial Solution for Quasi-linear Elliptic Equation with Critical growth[J].Sci.in China(Series A),1988,3:225-237.(in Chinese)

二级参考文献12

  • 1朱熹平.临界增长拟线性椭圆型方程的非平凡解[J].中国科学：A辑,1988,3:225-237.
  • 2Brezis H, Nirenberg L. Positive solutions of nonlinear elliptic equations involving critical Sobolev exponents [J]. 1983, 36: 437-477.
  • 3Mawhin J, Willem M. Positive solutions of nonlinear elliptic equations involving critical Sobolev exponents[J]. New York: Springer Verlag, 1989.
  • 4Tang Chun-lei, Wu Xing-ping. Existence and mulitiplicity of solution of semilinear elliptic equations [J].J. Math. Anal. Appl., 2001, 256: 1-12.
  • 5Azorero J G, Alonso I P. Some results about the existence of a second positive solution in a quasilinear critical problem [J]. Indian Univ. Math. J., 1994, 43: 941-957.
  • 6Jirk Bouchala, Pavel Drábek. Strong resonance for some quasilinear elliptic equations [J]. J. Math. Anal.Appl., 2000, 245: 7- 19.
  • 7Tang Chun-lei, Gao Qi-ju. Elliptic Resonant Problems at Higher Eigenvalues with an Unbounded Nonlinear Term [M]. Academic Press, 1998, 0022-0396.
  • 8Liu Shui-qiang, Tang Chun-lei, Wu Xing-ping. Multiplicity of nontrivial solutions of semilinear elliptic equations [J]. J. Math. Anal. Appl., 2000, 249: 289- 299.
  • 9Wu Xing-ping, Tang Chun-lei. Some existence theorems for elliptic resonant problems [J]. J. Math. Anal.Appl., 2001, 264: 133-146.
  • 10Liu Shui-qiang, Tang Chun-lei. Existence and multiplicity of solutions for a class of semilinear elliptic equations [J]. J. Math. Anal. Appl., 2001, 257: 321-331.

共引文献8

同被引文献5

  • 1饶若峰.具临界指数椭圆方程-Δu=λ_κu+|u|^(2^*-2)u+f(x,u)非平凡多解存在性[J].数学年刊（A辑）,2005,26(6):749-754. 被引量：12
  • 2[3]Chun-Lei Tang,Qi-Ju Gao.Elliptic Resonant Problems at Higher Eigenvalues with an Unbounded Nonlinear Term[J].Academic Press,1998,0022-0396.
  • 3[4]J Mawhin,M Willem.Critical Point Theory and Hamiltonian Systems[M].NewYork:Springer Verlag,1989.
  • 4[5]WA Strauss.Existence of Solitary Waves in Higher Dimensions[J].Comm MathPhys,1977,55:149-162.
  • 5[6]Wu Xingping,Tang Chunlei.Some Existence Theorems for Elliptic ResonantProblems[J].J Math Anal Appl,2001,264:133-146.

引证文献1

大学数学
2006年 第5期

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