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一类自然增长的拟线性椭圆型方程的非平凡解 被引量：1

Nontrivial Solution for a Class of Quasilinear Equation with Natural Growth
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摘要 本文利用不光滑泛函的临界点理论证明了与泛函 I(u)=∫_Ω[1/2a_(ij)(x,u)D_iuD_ju-G(x,u)]dx,G(x,u)=∫_0g(x,t)dt相对应的Euler-Lagrange方程齐次Dirichlet问题非平凡解的存在性.证明改进了对α_(ij)(x,u)与G(x,u)所加的条件. We use a nonsmooth critical point theory to prove the existence of non-trivial solutions of the homogeneous Dirichlet problem of Euler-Lagrange equation for functional We improve some conditions assumed on aij(x,u) and G(x,u).
作者 沈尧天
机构地区 华南理工大学应用数学系
出处 《数学学报（中文版）》 SCIE CSCD 北大核心 2003年第4期683-690,共8页 Acta Mathematica Sinica：Chinese Series
基金 国家自然科学基金(10171032) 广东省自然科学基金(011606)
关键词 自然增长 椭圆方程 非光滑泛函 临界点理论 Natural growth Elliptic equation Nonsmooth functional Critical theory
分类号 O175.25 [理学—基础数学]
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参考文献18

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同被引文献12

  • 1廖为,蒲志林.一类拟线性椭圆型方程Dirichlet问题正解的存在性[J].四川师范大学学报（自然科学版）,2007,30(1):31-35. 被引量：7
  • 2Ambrosetti A, Rabinowitz P. Dual variational methods in critical points theory and applications[J]. J Funct Anal,1973,14:349-381.
  • 3Costa D, Magalhaes C. Variational eUiptic problems which are nonquadrotic at infinity[ J ]. Nonl Anal, 1994,23:1401-1412.
  • 4Stuart C, Zhou H S. Communications in Partial Differential Equations, 1999,24 : 1731-1758.
  • 5Chang K C. J Math Anal Appl,1981,80:102-129.
  • 6Degiovanni M, Marzocchi M. A critical point theory for nonsmooth functional[ J ]. Ann Mat Puru Appl, 1994,167 (4) :73-100.
  • 7Corvellec J N, Degiovanni M, M arzocchi M. Topoi Methods Nonlinear Anal, 1993,1 : 151-171.
  • 8Areoya D, Boeeardo L. Arch Rat Meth Anal,1996,134:249-274.
  • 9Gladkov A, Slepchenkov N. Entire solutions of quasilinear elliptic equations[ J]. Nonl Anal,2007,66:750-775.
  • 10Mihailescu M, Pucci P, Radulescu V. J Math Anal Appl,2008 ,340 :687-698.

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数学学报（中文版）
2003年 第4期

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