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方程—Δu=f(x,u,Du)在W^(2, P)(Ω)中的可解性 被引量:1

The Solvability of the Equation -Δu=f(x,u,Du) in W^(2, p) (Ω)
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摘要 本文在一定的条件下证明了DiriChlet问题■在W^(2,p)(Ω)中的可解性,其中p>1当N=1或2;P≥2N/(N+2)当N≥3,而不象以前关于这方面的工作要限制p>N。 The present paper proves that under certain assumptions on f the Dirichlet problem is solvable in W^(2,p)(Ω) with p>1 when N=1, 2 and p≥2N/(N+2) when N≥3, which is different from the other papers on this problem in that they are all limited to p>N.
作者 严子谦
机构地区 吉林大学数学系
出处 《吉林大学自然科学学报》 CSCD 1992年第2期30-32,共3页 Acta Scientiarum Naturalium Universitatis Jilinensis
关键词 椭圆方程 可解性 不动点定理 elliptic equations solvability fixed point theorem
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  • 1Amann H, Crandall M G. On Some Existence Theorems for Semilinear Elliptic Equations [ J ]. Indiana Univ Math J, 1978, 27: 779-790.
  • 2Pohozaev S. On Equations of the Type A u =f(x,u,Du) [J]. Mat Sb, 1980, 113: 324-338.
  • 3Xavier J B M. Some Existence Theorems for Equations of the Form -Δ u =f(x,u,Du) [J]. Nonlinear Analysis TMA, 1990, 15(1) : 59-67.
  • 4WANG Xu-jia, DENG Yin-bing. Existence of Muhiple Solutions to Nonlinear Elliptic Equations in Nondivergence Form [J]. J Math Anal and Appl, 1995, 189(3) : 617-630.
  • 5YAN Zi-qian. A Note on the Solvability in W2,p (Ω) for the Equation - Δ u =f(x,u,Du) [ J]. Nonlinear Analysis TMA, 1995, 24(9): 1413-1416.
  • 6Figuereido D G, de, Girardi M, Matzeu M. Semilinear E11ptic Equations with Dependence on the Gradient via Mountain-Pass Techniques [ J ]. Differential and Integral Equations, 2004, 17:119-126.
  • 7Girardi M, Matzeu M. A Compactness Result for Quasilinear Elliptic Eqations by Mountain Pass Techniques [ J]. Rend Math Appl, 2009, 29 (1) : 83-95.
  • 8Servadei R. A Semilinear Elliptic PDE Not in Divergence Form via Variational Methods [ J]. J Math Anal Appl, 2011, 383 ( 1 ) : 190-199.
  • 9Girardi M, Matzeu M. Existence of Periodic Solutions for Some Second Order Quasilinear Hamiltonian Systems [ J ]. Rend Lincei Mat Appl, 2007, 18(1) : 1-9.
  • 10TENG Kai-min, ZHANG Chao. Existence of Solution to Boundary Value Problem for Impulsive Differential Equations [J]. Nonlinear Anal RWA, 2010, 11(5) : 4431-4441.

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