Positive rotationally symmetric solutions for a Dirichlet problem involving the higher mean curvature operator in Minkowski space
The paper deals with the global behavior of positive rotationally symmetric solutions to a Dirichlet problem involving the \(k\)-th mean curvature operator in the Minkowski space \(\mathbb{L}^{n+1}.\) Precisely, the authors study the structure of positive (or negative) solutions to the problem \[ \big(r^{n-k}\phi^k(v')\big)'=\lambda n r^{n-1} H_k(v(r),r), \quad r\in (0,R), \] \[ |v'|<1,\quad r\in(0,R), \] \[ v'(0)=0=v(R), \] where \(\lambda\) is a positive parameter, \(\phi(s)=s/\sqrt{1-s^2}\) and \(H_k\) is a given continuous function. The proofs make use of global bifurcation techniques.
scientific article; zbMATH DE number 6824850
scientific article