Exact multiplicity and ordering properties of positive solutions of a \(p\)-Laplacian Dirichlet problem and their applications.
The authors discuss the exact multiplicity and ordering properties of positive solutions to a nonlinear one-dimensional Dirichlet problem associated with the p-Laplacian, where p is greater than 1. This extends a result of \textit{S.-H. Wang} and \textit{D.-M. Long} [Nonlinear Anal., Theory Methods Appl. 44A, No. 4, 469--486 (2001; Zbl 0992.34014)], where the case p=2 was considered. The theory is applied to the study of a Dirichlet problem with polynomial nonlinearities, and to that of a stationary singular diffusion problem.
scientific article; zbMATH DE number 2022063