Multiple solutions for a semilinear boundary value problem: A computational multiplicity proof (Q1593769)

In the paper there is with unstandard advance proved the following theorem: Let \(\Omega= (0,1)\times(0,1)\). The boundary value problem \[ \Delta u= u^2= s\sin\pi x\cdot\sin\pi y\quad\text{in }\Omega, \] \[ u|_{\partial\Omega}= 0, \] has at least four solutions for \(s= 800\).