The extremes sit on the boundary

Let u = u(x, y) be the solution of the boundary value problem ${\partial }^{2}u/\partial x^2+{\partial }^{2}u/\partial y^2=0$ on (0, 1) × (0, 1), with $u(x,0)=e^{(}\pi x),u(x,1)=-e^{(}\pi x)$ for $x\in [0,1],u(0,y)=\cos (\pi y)+\sin (\pi y)$ and $u(1,y)=e^{\pi }(\cos (\pi y)+\sin (\pi y))$ for y ∈ [0, 1]. Then there exists a point $(x_0,y_0)\in (0,1)\times (0,1)$ such that