A note on additional properties of sign changing solutions to superlinear elliptic equations

Abstract

We obtain upper bounds for the number of nodal domains of sign changing solutions of semilinear elliptic Dirichlet problems using suitable min-max descriptions. These are consequences of a generalization of Courant's nodal domain theorem. The solutions need not to be isolated. We also obtain information on the Morse index of solutions and the location of sub- and supersolutions.