Special Session 15: Qualitative properties for solutions to nonlinear elliptic and parabolic equations
Uniqueness of entire solutions to quasilinear equations with a sub-natural growth term and measure data
Phuc C Nguyen
Louisiana State University USA
Co-Author(s): Igor E. Verbitsky
Abstract:
We present the uniqueness of nontrivial solutions to the problem
\begin{equation*}
\left\{ \begin{array}{ll}
- \Delta_p u = \sigma u^q + \mu, \quad u\geq 0 \quad \text{in } \mathbb{R}^n, \
\displaystyle{\liminf_{|x|\rightarrow \infty}}\, u = 0,
\end{array}
\right.
\end{equation*}
in the sub-natural growth case $0