Gvazava, Dzhondo On the Cauchy problem for an equation of surface theory. (Russian. English summary) Zbl 0565.35020 Differ. Uravn. Primen. 34, 9-15 (1983). It is shown that the Cauchy problem for the equation \((1+u^ 2_ y)u_{xy}-u_ xu_ yu_{yy}=0\) with initial conditions on the free curve has as many solutions as some nonlinear functional equation. To each solution there corresponds a unique domain of existence. MSC: 35G25 Initial value problems for nonlinear higher-order PDEs 35A05 General existence and uniqueness theorems (PDE) (MSC2000) Keywords:equation of surface theory; multiplicity of solutions; Cauchy problem; existence PDFBibTeX XMLCite \textit{D. Gvazava}, Differ. Uravn. Primen. 34, 9--15 (1983; Zbl 0565.35020)