In this paper we consider the equation u (t) = f (t, u(t), u (t)) and prove the unique solvability of the Cauchy problem u(0) = 0, u (0) = λ with λ > 0.

Scattering problems in periodic waveguides are interesting but also challenging topics mathematics both theoretically and numerically. As is well known, the unique solvability of these ...

In this article we cast the unique solvability of a class of nonautonomous kinetic equations in terms of evolution systems, generalizing semigroup results pertaining to the corresponding autonomous kinetic equations. AMS Subject Classification: 47N55, 82C70

We prove the unique solvability of a mixed boundary value problem for the p -Laplace operator by means of variational methods. Using the obtained results, we construct an iterative procedure for solving the Cauchy problem for the p -Laplace operator.

This paper is concerned with a mean-field linear quadratic (LQ, for short) optimal control problem with deterministic coefficients. It is shown that convexity of the cost functional is necessary for the finiteness of the mean-field LQ problem, whereas uniform convexity of the cost functional is sufficient for the open-loop solvability of the problem. By considering a family of uniformly convex ...

This article investigates the solvability of volume integral equations arising in elastodynamic scattering by penetrable obstacles. The elasticity tensor and mass density are allowed to be smoothly heterogeneous inside the obstacle and may be discontinuous across the background-obstacle interface, the background elastic material being homogeneous. Both materials may be anisotropic, within certa...