数学分析dubuxianqing06/21 15:081 条评论2008年中科大数学分析无解真题设∂Ω≜{(x,y)∈R2:x2+y2=1}.\partial \Omega \triangleq \left\{ \left( x,y \right) \in \mathbb{R}^{2} :x^{2}+y^{2}=1 \right\}.∂Ω≜{(x,y)∈R2:x2+y2=1}.若f∈C2(R2)f\in C^{2}\left( \mathbb{R}^{2} \right)f∈C2(R2)满足f∣∂Ω=0,limx→+∞f(x,0)=1.f|_{\partial \Omega}=0,\lim_{x\rightarrow +\infty} f\left( x,0 \right) =1.f∣∂Ω=0,x→+∞limf(x,0)=1.证明:存在(x0,y0)∈R2\left( x_{0},y_{0} \right) \in \mathbb{R}^{2}(x0,y0)∈R2使得(Δf)(x0,y0)⩾0\left( \Delta f \right) \left( x_{0},y_{0} \right) \geqslant 0(Δf)(x0,y0)⩾0.