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

Thomas Bartsch, Tobias Weth

DOI: http://dx.doi.org/10.12775/TMNA.2003.025


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.


Sign changing solutions; nodal domains; Morse index; subsolution; supersolution

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