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We obtain upper bounds for the number of nodal domains of signchanging solutions of semilinear elliptic Dirichlet problems usingsuitable min-max descriptions. These are consequences of ageneralization of Courant's nodal domain theorem. The solutions neednot to be isolated. We also obtaininformation on the Morse index of solutions and the location of sub- and supersolutions.

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