منابع مشابه
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.
متن کاملUniqueness Theorems for Cauchy Integrals
If μ is a finite complex measure in the complex plane C we denote by C its Cauchy integral defined in the sense of principal value. The measure μ is called reflectionless if it is continuous (has no atoms) and C = 0 at μ-almost every point. We show that if μ is reflectionless and its Cauchy maximal function Cμ ∗ is summable with respect to |μ| then μ is trivial. An example of a reflectionless m...
متن کامل$L_{p;r} $ spaces: Cauchy Singular Integral, Hardy Classes and Riemann-Hilbert Problem in this Framework
In the present work the space $L_{p;r} $ which is continuously embedded into $L_{p} $ is introduced. The corresponding Hardy spaces of analytic functions are defined as well. Some properties of the functions from these spaces are studied. The analogs of some results in the classical theory of Hardy spaces are proved for the new spaces. It is shown that the Cauchy singular integral operator is...
متن کاملUnconditional 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...
متن کاملExistence and Uniqueness to the Cauchy Problem for Linear and Semilinear Parabolic Equations with Local Conditions
We consider the Cauchy problem in R for a class of semilinear parabolic partial differential equations that arises in some stochastic control problems. We assume that the coefficients are unbounded and locally Lipschitz, not necessarily differentiable, with continuous data and local uniform ellipticity. We construct a classical solution by approximation with linear parabolic equations. The line...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Memoirs of the Faculty of Science, Kyushu University. Series A, Mathematics
سال: 1971
ISSN: 1883-2172,0373-6385
DOI: 10.2206/kyushumfs.25.167