کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
6417296 | 1338685 | 2011 | 28 صفحه PDF | دانلود رایگان |
We study the qualitative behavior of non-negative entire solutions of differential inequalities with gradient terms on the Heisenberg group. We focus on two classes of inequalities: ÎÏu⩾f(u)l(|âu|) and ÎÏu⩾f(u)âh(u)g(|âu|), where f, l, h, g are non-negative continuous functions satisfying certain monotonicity properties. The operator ÎÏ, called the Ï-Laplacian, generalizes the p-Laplace operator considered by various authors in this setting. We prove some Liouville theorems introducing two new Keller-Osserman type conditions, both extending the classical one which appeared long ago in the study of the prototype differential inequality Îu⩾f(u) in Rm. We show sharpness of our conditions when we specialize to the p-Laplacian. While proving these results we obtain a strong maximum principle for ÎÏ which, to the best of our knowledge, seems to be new. Our results continue to hold, with the obvious minor modifications, also for Euclidean space.
Journal: Journal of Differential Equations - Volume 250, Issue 6, 15 March 2011, Pages 2643-2670