Radial oscillatory solutions of some quasi-linear elliptic equations (Q1767851)

The authors deal with the generalized \(p\)-Laplacian equation \[ \text{div}(|Du|^{p-2}Du)+ f(u)=0, \quad x\in\mathbb R^n. \tag{1} \] They are interested in the asymptotic behaviour of oscillatory solutions with a prescribed number of zeros by a scaling argument and obtain precise estimates of the gap between the successive zeros, which improve and extend some of the results existing in the literature [\textit{F. B. Weissler}, J. Differ. Equations 83, 368--378 (1990; Zbl 0695.34020), \textit{L. F. Ho}, Nonlinear Anal., Theory Methods Appl. 41, No. 5--6 (A), 573--589 (2000; Zbl 0962.34019)].