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Existence of the Positive Solutions for A Class of Nonlinear Elliptic Equations

Author: WangPeng
Tutor: PuZhiLin
School: Sichuan Normal University
Course: Computational Mathematics
Keywords: Elliptic equation Variational methods Improving Hardy inequality
CLC: O175.25
Type: Master's thesis
Year: 2010
Downloads: 10
Quote: 0
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Abstract


In this paper,we study the existence of nontrivial solutions for a class of second elliptic equation with critical potential and indefinite weights in RN. where 2≤p*<2N/(N-2).0≤μ≤μ(?)1/4, f(x,u) satisfies following condition: (H.1)f(x,u):Ω×R→R is continuous,and f(x.0)=0: (H.2)limu→0 f(x,u)/u=k(x)∈L∞(Ω),|k(x)|∞=λ1 (H.3)limu→∞f(x,u)/|u|p*-1=0. We use critical point theory.and Hardy inequality prove the existence of non-trivial solution for a class of second elliptic equation with critical potential and indefinite weights in RN

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CLC: > Mathematical sciences and chemical > Mathematics > Mathematical Analysis > Differential equations, integral equations > Partial Differential Equations > Elliptic equations
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