Multiplicity of 2-nodal solutions for semilinear elliptic problems in RN

In this paper, we study the effect of the graph of weight functions on the number of 2-nodal solutions for semilinear elliptic problems in RN. Our results generalize and improve on the results of [D. Cao, E.S. Noussair, Multiplicity of positive and nodal solutions for nonlinear elliptic problems in RN, Ann. Inst. H. Poincaré Anal. Non Linéaire 13 (5) (1996) 567–588]. In the present paper, we give a new analytical method to study this issue.