Some remarks on the critical point theory (Q933129)

The author considers elliptic equation with Dirichlet boundary condition: \[ -\Delta u=f(x,u),\;x\in\Omega\quad u=0\;x\in\partial \Omega,\tag{1} \] where \(\Omega\) is a bounded domain in \(\mathbb{R}^N\) with smooth boundary \(\partial\Omega\). The author deals with the existence and multiplicity results for (1). To this end the author uses Morse theory and minimax method which leads to a more precise description of topological construction of level set of critical value of energy functional for mountain pass critical point.