Uniqueness for a nonlinear abstract Cauchy problem

Inhomogeneous Two-Parameter Abstract Cauchy Problem

A singular abstract cauchy problem.

In this note a singular abstract Cauchy problem is considered. A solution is obtained for this problem in terms of a regular abstract Cauchy problem. As an application we obtain a new solution of the initial value problem for a class of singular partial differential equations.

inhomogeneous two-parameter abstract cauchy problem

Uniqueness Theorem for a Cauchy Problem with Hysteresis

The Cauchy problem for an ordinary differential equation coupled with a hysteresis operator is studied. Under physically reasonable assumptions on the forcing term, uniqueness of solutions is shown without assuming Lipschitz continuity of the hysteresis curves. The result is true for any kind of hysteresis operators with monotone curves of motion.

Unconditional Uniqueness of Solution for the Cauchy Problem of the Nonlinear Schrödinger Equation

where λ ∈ C and T > 0. Let α > 0 and s ≥ 0 be specified later, and let u0 ∈ H. Suppose that u ∈ C([0, T ];H) with (2) and u satisfies equation (1) in D0((0, T )× R), that is, in the distribution sense. We briefly recall known results on the uniqueness of solution for (1)-(2). In [3], Ginibre and Velo prove that if s = 1 and α < 4/(n− 2), the solution is unique. In [2], Cazenave and Weissler sho...