Three positive solutions for nonlinear elliptic equations in finite strip with hole (Q1766735)

The author considers the following nonlinear elliptic equation \[ -\Delta u+ u= |u|^{p-2} u\quad\text{in }\Omega,\qquad u\in H^1_0(\Omega),\tag{1} \] where \(\Omega\) is a domain in \(\mathbb{R}^N\) and interested in the effect of the domain on the multiplicity of positive solutions for (1). To this end, the author uses the Ekeland variational principle and the center mass function, which lead to the existence at least of three positive solutions for (1) in finite strip with holes.