Electronic Journal of Differential Equations, 
Vol. 2021 (2021), No. 30, pp. 1-9.

Title: Positive solutions to a Dirichlet problem with non-Lipschitz nonlinearities
       
Author: Giovanni Anello (Univ. of Messina, Italy)

Abstract:
 Let &Omega; be a bounded smooth domain in R<sup>N<'sup>.
 We study the existence of positive solutions to the Dirichlet problem
 $$\displaylines{
 -\Delta u=(1-u)u^{s-1}-\lambda u^{r-1}, \quad\text{in } \Omega,\cr
 u=0, \quad \text{on } \partial\Omega,
 }$$
 where 1&lt;r&lt;s&le;2, and &lambda;&gt;0. In particular, we answer to some questions posed
 in the recent paper [3] where this problem was considered.

Submitted October 1, 2020. Published April 20, 2021.
Math Subject Classifications: 35J20, 35J25.
Key Words: Positive solution; non-Lipschitz nonlinearity; variational methods.