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- W2023846049 abstract "The aim of this paper is to study the qualitative behaviour of non-negative entire solutions of certain differential inequalities involving gradient terms on the Heisenberg group. We focus our investigation on the two classes of inequalities of the form $Delta^phi u ge f(u)l(|nabla u|)$ and $Delta^phi u ge f(u) - h(u) g(|nabla u|)$, where $f,l,h,g$ are non-negative continuous functions satisfying certain monotonicity properties. The operator $Delta^phi$, called the $phi$-Laplacian, can be viewed as a natural generalization of the $p$-Laplace operator recently 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 $Delta u ge f(u)$ in $erre^m$. Furthermore, we show sharpness of our conditions when we specialize to the case of the $p$-Laplacian. Needless to say, our results continue to hold, with the obvious minor modifications, also in the Euclidean space." @default.
- W2023846049 created "2016-06-24" @default.
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- W2023846049 date "2010-03-30" @default.
- W2023846049 modified "2023-09-27" @default.
- W2023846049 title "Keller-Osserman type conditions for differential inequalities with gradient terms on the Heisenberg group" @default.
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