Eigenvalue problems for some nonlinear Wheeler-DeWitt operators
The paper concerns the nonlinear PDE \[ {1\over x^2} {\partial^2\psi\over \partial y^2}- {\partial^2\psi\over \partial x^2}- {p\over x} {\partial\psi\over \partial x}+ (x^2- k^2 x^2+ gx^{q- 2}|\psi|^r)\psi= 0. \] Here \(g, p, y\in \mathbb{R}\), \(x\in (0, R)\), \(R> 0\), \(r> 0\), \(2q\geq rp\). The authors prove existence and nonexistence results for special solutions of the form \(\psi(x, y)= e^{i\mu y} u(x)\), \(\mu\in \mathbb{R}\).
scientific article; zbMATH DE number 811431