On solutions of first-order partial differential-functional equations in an unbounded domain
Under the assumptions of continuity and the existence of first-order partial derivatives of the solutions it is proved that the Cauchy problem \[ z_ x^{(i)}(x,y)=f^{(i)}(x,y,z(x,y),z,z_ y^{(i)}(x,y)); \] \[ z^{(i)}(x,y)=\phi_ i(x,y)\quad for\quad (x,y)\in [-\tau_ 0,0]\times {\mathbb{R}}^ n\quad (i=1,...,m) \] admits at most one solution if the function \(f=(f^{(i)},...,f^{(m)})\) of the variables (x,y,p,z,q) satisfies a Lipschitz condition with respect to (p,z,q), or a Lipschitz condition with respect to (p,z) and a Hölder condition with respect to q.
scientific article; zbMATH DE number 4073624