Multiplicity of nodal solutions for elliptic problems involving non-odd nonlinearities

In this paper, we study the effect of domain shape on the number of 2-nodal solutions for the semilinear elliptic equation involving non-odd nonlinearities. We prove that a semilinear elliptic equation in an m$m$-bump domain (possibly unbounded) has m²$m^2$ 2-nodal solutions and we can find a least energy nodal solution in those solutions. Furthermore, we can describe the bump location of these solutions.