A note on additional properties of sign changing solutions to superlinear elliptic equations
The authors deal with sign-changing solutions of the semilinear Dirichlet problem \[ -\Delta u=f(x,u) \quad\text{for }x\in\Omega, \qquad u=0 \quad\text{for }x\in\partial\Omega, \] where \(\Omega\) is a bounded smooth domain in \(\mathbb R^N\), \(N\geq 2\). Under some natural assumptions on \(f\), the authors using suitable min-max descriptions obtain upper bounds for the number of nodal domains of sign changing solutions for (1). Moreover, they also obtain information on the Morse index of solutions and the location of sub- and supersolutions.
scientific article; zbMATH DE number 2096714