Positive weak solutions of uniformly elliptic inequalities and applications to population models.

By using the uniformly ellipticity of linear partial differential operators (which contain p-Laplacian operators with $ 1 \lt p \lt \infty $ 1 < p < ∞), weak comparison principle and Urysohn's lemma, in the paper, we introduce and study a class of new variational inequalities involving uniformly elliptic operators and demicontinuous S-contractive operators to extend some corresponding tasks and scope on population genetics. Further, as applications, we employ the main results presented in this paper to second-order uniformly elliptic inequalities and a population model of one species arising in disrupted environments. [ABSTRACT FROM AUTHOR]