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

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.