Special Session 54: Trends in Nonlinear Analysis

Liouville properties for differential inequalities with $(p,q)$ Laplacian operator
Mousomi Bhakta
Indian Institute of Science Education and Research Pune (IISER Pune)
India
Co-Author(s):    Anup Biswas, Roberta Filippucci
Abstract:
We will discuss several Liouville-type theorems for nonnegative solutions associated with a class of nonhomogenenous quasilinear inequalities, namely \begin{equation*}\tag{$P_s$} -\Delta_p u-\Delta_q u\geq u^{s-1} \, \text{ in }\, \Omega, \end{equation*} where $p>q>1$, $s>1$ and $\Omega$ is any exterior domain of $\mathbb{R}^N$ and \begin{equation*}\tag{$P_{sm}$} -\Delta_p u-\Delta_q u \geq u^s |\nabla u|^m \quad \text{ in }\mathbb{R}^N, \end{equation*} where $p>q>1$, $N>q$ and $s, \, m\geq 0$.