Semilinear Neumann boundary value problems on a rectangle
Semilinear Neumann boundary value problems on a rectangle
We consider a semilinear elliptic equation \begin{equation*} \Delta u+\lambda f(u)=0, \;\; \mathbf {x}\in \Omega ,\;\; \frac {\partial u}{\partial n }=0, \;\; \mathbf {x}\in \partial \Omega , \end{equation*} where $\Omega$ is a rectangle $(0,a)\times (0,b)$ in $\mathbf {R}^2$. For balanced and unbalanced $f$, we obtain partial descriptions of global bifurcation diagrams …