Special Session 14: New perspectives in the qualitative study of nonlinear differential equations and dynamical systems

Nodal solutions for the Minkowski mean curvature operator: multiplicity and large-$\mu$ asymptotics
Ricardo Ziegele
Universit\\`{a} degli studi di Torino
Italy
Co-Author(s):    Alberto Boscaggin, Francesca Colasuonno
Abstract:
We study the Dirichlet problem for the mean curvature operator in Minkowski space on a bounded domain $\Omega \subset \mathbb{R}^n$. For this problem, we study the interaction between two parameters $(\lambda,\mu)$ and ther effects on the multiplicity of nodal solutions. In the general setting, using non-smooth variational methods, we prove the existence of a ground-state solution and a linking solution. In the radial case, we prove existence and multiplicity of nodal solutions. Finally, we characterize the limiting profile of these solutions in both settings as $\mu \to +\infty$. \medskip \noindent This is a joint work with Alberto Boscaggin (Universit\`a di Torino) and Francesca Colasuonno (Universit\`a di Torino).