Four 2-nodal solutions for a semilinear elliptic equation in a finite strip with a hole

In this paper, we study the decomposition of the filtration of the Nehari manifold via the variation of domain shape. We use this result to prove that the semilinear elliptic equation in a finite strip with hole has at least four 2-nodal solutions (solutions with precisely two nodal domains). Furthermore, we can describe the bump location of these solutions.