Approximation of solutions of differential equations in Hilbert space
نویسندگان
چکیده
منابع مشابه
$L^p$-existence of mild solutions of fractional differential equations in Banach space
We study the existence of mild solutions for semilinear fractional differential equations with nonlocal initial conditions in $L^p([0,1],E)$, where $E$ is a separable Banach space. The main ingredients used in the proof of our results are measure of noncompactness, Darbo and Schauder fixed point theorems. Finally, an application is proved to illustrate the results of this work.
متن کاملApproximation of Solutions of Nonlinear Equations of Hammerstein Type in Hilbert Space
Let H be a real Hilbert space. Let F : D(F ) ⊆ H → H, K : D(K) ⊆ H → H be bounded monotone mappings with R(F ) ⊆ D(K), where D(F ) and D(K) are closed convex subsets of H satisfying certain conditions. Suppose the equation 0 = u + KFu has a solution in D(F ). Then explicit iterative methods are constructed that converge strongly to such a solution. No invertibility assumption is imposed on K, a...
متن کاملHilbert Space Methods for Partial Differential Equations
i Preface This book is an outgrowth of a course which we have given almost periodically over the last eight years. It is addressed to beginning graduate students of mathematics, engineering, and the physical sciences. Thus, we have attempted to present it while presupposing a minimal background: the reader is assumed to have some prior acquaintance with the concepts of " linear " and " continuo...
متن کاملAsymptotic Behavior and Stability of the Solutions of Functional Differential Equations in Hilbert Space
In the following article we present the results on the asymptotic behavior and stability of the strong solutions for functional differential equations (FDE). We also formulate several results on spectral properties (completeness and basisness) of exponential solutions of the above-mentioned equations. It is relevant to underline that our approach for researching FDE is based on the spectral ana...
متن کاملExistence of Solutions to Projected Differential Equations in Hilbert Spaces
We prove existence and uniqueness of integral curves to the (discontinuous) vector field that results when a Lipschitz continuous vector field on a Hilbert space of any dimension is projected on a non-empty, closed and convex subset.
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: Journal of the Mathematical Society of Japan
سال: 1973
ISSN: 0025-5645
DOI: 10.2969/jmsj/02510132