A note on additional properties of sign changing solutions to superlinear elliptic equations
Thomas Bartsch, Tobias Weth · Topological Methods in Nonlinear Analysis · 2003
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.