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Mathematics Colloquium - Ratnasingham Shivaji, Univ of North Carolina at Greensboro
April 18, 2025
2pm - 3pm
Access & Features
- Free food
- Open to the public
Title: Uniqueness of Positive Solutions for a Class of Nonlinear Elliptic Equations with Robin Boundary Conditions
Abstract: We prove uniqueness of positive solutions to the BVP
\[
\begin{cases}
-\Delta u= \lambda f(u)\quad \text{in } \Omega,\\
\frac{\partial u}{\partial n}+ bu =0\quad \text{on } \partial\Omega,
\end{cases}
\]
when the parameter $\lambda$ is large independent of $b\in (0,\infty)$. Here $\Omega$ is a bounded domain in $\mathbb{R}^n$ with smooth boundary $\partial\Omega$, $f:[0,\infty)\to [0,\infty)$ is continuous, concave for $u$ large, and sublinear at $\infty$. This is a joint work with D.D. Hai and Xiao Wang.
Sponsored by: Mathematics
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Junping Shi