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一类非线性奇异椭圆方程解的存在性和多重性 被引量：1

Existence and Multiplicity of Solutions for a Nonlinear Singular Elliptic Equation
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摘要 研究一类具奇性和退化性的非线性椭圆方程Dirichlet问题,通过构造适当的逼近问题并结合紧致方法,证明了解的存在性和多重性. This paper is devoted to the existence and multiplicity of the solutions of the homogenous Dirichlet problem for a nonlinear singular elliptic equation with natural growth in the gradient. The proofs for the main results are based on a prior estimate of the solutions of approximate problems and compactness techniques.
作者 魏晓丹
机构地区 大连民族学院计算机科学与技术学院
出处 《吉林大学学报（理学版）》 CAS CSCD 北大核心 2008年第4期653-654,共2页 Journal of Jilin University:Science Edition
基金 国家自然科学基金(批准号:10626056) 大连民族学院人才引进基金(批准号:20076209)
关键词 奇异椭圆方程 解 存在性 多重性 singular elliptic equation solution existence multiplicity
分类号 O175.25 [理学—基础数学]
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参考文献7

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  • 2Boccardo L, Murat F, Puel J P. L^∞ Estimate for Some Nonlinear Elliptic Partial Differential Equations and Application to an Existence Result [J]. SIAM J Math Anal, 1992, 2(23) : 326-333.
  • 3Ferone V, Posteraro M R, Rakotoson J M. L^∞ -Estimates for Nonlinear Elliptic Problems with p-Growth in the Gradient [J]. J of Inequal and Appl, 1999, 3(2) : 109-125.
  • 4Grenon N. Existence and Comparison Results for Quasilinear Elliptic Equations with Critical Growth in the Gradient [ J ]. Journal of Differential Equations, 2001, 171 ( 1 ) : 1-23.
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同被引文献7

  • 1袁洪君,陈明涛.一类具有退化性和奇异性的拟线性椭圆方程正解的注记[J].吉林大学学报（理学版）,2005,43(6):741-745. 被引量：1
  • 2Bensoussan A, Boccardo L, Murat F. On a Nonlinear Partial Differential Equation Having Natural Growth Terms and Unbounded Solution [ J]. Ann Inst H Poincare Anal Nonlineaire, 1988, 5 (4) : 347-364.
  • 3Boccardo L, Gallouet T. Strongly Nonlinear Elliptic Equations Having Natural Growth Terms and L1 Data [ J ]. Nonlinear Anal: Theory, Methods & Applications, 1992, 19(6) : 573-579.
  • 4Arcoya D, Baffle S, Martinez-Aparicio P J. Singular Quasilinear Equations with Quadratic Growth in the Gradient without Sign Condition [J]. J Math Anal Appl, 2009, 350( 1 ): 401-408.
  • 5Arcoya D, Martinez-Aparicio P J. Quasilinear Equations with Natural Growth [ J ]. Rev Mat Iberoamericana, 2008, 24(2) : 597-616.
  • 6Arcoya D, Carmona J, Leonori T. Existence and Nonexistence of Solutions for Singular Quadratic Quasilinear Equations [J]. J Differential Equations, 2009, 246(10) : 4006-4042.
  • 7Arcoya D, Ruiz D. The Ambrosetti-Prodi Problem for the p-Laplace Operator [ J ]. Commu Partial Diff Equa, 2006, 31 (6) : 849-865.

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吉林大学学报（理学版）
2008年 第4期

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