On \(x\)-analytic solutions to the Cauchy problem for partial differential equations with retarded variables
Summary: We prove some existence results for solutions analytic with respect to the spatial variables to the Cauchy problem for the first-order equation \[ D_t u(t, x)= g(t, x, u(\alpha(t), \beta(t, x)), D_x u(\gamma(t), \delta(t, x))) \] with a dealy and some deviations not only at the function, but also at its derivative. We construct a natural Banach space and a norm which make an adequate integral operator contractive. Due to a useful relation of partial order in this space the main problem is also placed in the theory of monotone iterative techniques.
scientific article; zbMATH DE number 889001