Existence and nonexistence of positive solutions of quasi-linear elliptic equations with gradient terms

2018/08/20 by Dania Morales, Morales, Dania
Mathematics · #Analysis of PDEs (math.AP) #FOS: Mathematics #math.AP

paper · pdf · doi:10.48550/arxiv.1808.06561

arxiv created 2018/08/20 · arxiv updated 2018/08/21

Abstract

We study the existence and nonexistence of positive solutions in the whole Euclidean space of coercive quasi-linear elliptic equations such as Δ_p u = f(u)± g(|∇ u|) where f∈ C([0,∞)) and g∈ C^0,1([0,∞)) are strictly increasing with f(0)=g(0)=0. Among other things we obtain generalized integral conditions of Keller-Osserman type. In the particular case of plus sign on the right-hand side we obtain that different conditions are needed when p≥ 2 or p≤ 2, due to the degeneracy of the operator.

Related

• Solvability of nonlinear elliptic equations with gradient terms
• Existence of positive solutions to quasi-linear elliptic equations with exponential growth in the whole Euclidean space
• On the positive solutions to some quasilinear elliptic partial differential equations
• An existence result for a quasilinear system with gradient term under the Keller-Osserman conditions
• A priori estimates and Liouville type results for quasilinear elliptic equations involving gradient terms