On the set of solutions of boundary value problems for hyperbolic differential equations (Q5927572)

The author considers a system \(u_{xy} = f(x,y,u,u_x,u_y,u_{xy})\) with a Carathéodory map \(f:[0,p_1]\times [0,p_2]\times(\mathbb R^n)^4\to\mathbb R^n\). The boundary conditions determine Floquet, Nicoletti or Nicoletti--Floquet problems. It is shown that the sets of solutions for these problems are nonempty, convex and compact in \(C\)-norm. Additional conditions ensure the applicability of the Browder-Göhde-Kirk fixed point theorem.