A general solution of the functional equation $\int_{0}^{\infty }f(x+y)d\mu (y)$ = f(x) where f is a nonnegative function and μ is a σ-finite positive Borel measure on [0, ∞) is shown to be f(x) = p(x ...

This is a preview. Log in through your library . Abstract The Cauchy problem for a nonlinear functional differential equation is considered. A theorem on the existence of classical solutions defined ...

Cauchy problems and inverse problems in partial differential equations (PDEs) represent a class of challenging mathematical models where one seeks to determine unknown data inside a domain from ...

The Cauchy problem for the Helmholtz equation has emerged as an important yet challenging subject in applied mathematics and engineering. This problem involves deducing interior solutions from ...