Special Session 141: New trends and methods for differential problems

Uniqueness for Neumann problems for nonlinear elliptic equations with lower order terms
Maria Rosaria MR Posteraro
University of Naples Federico II
Italy
Co-Author(s):    M.F.Betta, O. Guib\`e, A. Mercaldo
Abstract:
We prove uniqueness results for weak solutions to a class of Neumann problems, whose prototype is \begin{gather*} \begin{cases} \null \lambda (1+ u^2)^{(p-2)/2}u-\diw((1+|\nabla u|^2)^{(p-2)/2} \nabla u) & \qquad\ - \diw(c(x) (1+|u|^2)^{(\tau+1)/2}) +b(x) (1+|\nabla u|^2)^{(\sigma+1)/2}=f &\text{ in } \Omega\ \left( (1+|\nabla u|^2)^{(p-2)/2} \nabla u + c(x) (1+|u|^2)^{(\tau+1)/2}) \right)\cdot\underline n=0 & \text{on}\ \partial \Omega \,, \end{cases} \end{gather*} where $\Omega$ is a bounded open subset of $\R^N$ $(N\ge 2)$ with Lipschitz boundary, $p$ is a real number $\frac{2N}{N+1}< p