Results 91 to 100 of about 219,754 (206)
Abstract Cauchy problems for second order linear differential equations in a Banach space
Hiroshima Mathematical Journal, 1987 Let A be a closed linear operator in a Banach space X and let Y be a linear manifold of X. Assume that (a) Y is a normed space under a certain norm \(\|| \cdot \||\) which is stronger than the original norm \(\| \cdot \|\) of X; (b) there is \(\omega \geq 0\) such that for each \(\lambda >\omega\), the range \(R(\lambda^ 2-A)\) contains Y, \(R(\lambda^
Takenaka, Tosiharu, Okazawa, Noboru
openaire +2 more sources
Generalized contraction principle under relatively weaker contraction in partial metric spaces
Advances in Difference Equations, 2019 In this paper, we introduce the concept of a generalized weak (ϕ,R) $(\phi,\mathcal{R})$-contraction and employ this to prove some fixed point results for self-mappings in partial metric spaces endowed with a binary relation R $\mathcal{R}$.
Atiya Perveen +2 more
doaj +1 more source
Weak Solutions of Abstract Evolutionary Integro-Differential Equations in Hilbert Spaces
Funkcialaj Ekvacioj, 2009 We prove existence and uniqueness of weak solutions to certain abstract evolutionary integro-differential equations in Hilbert spaces, including evolution equations of fractional order less than 1. Our results apply, e.g., to parabolic partial integro-differential equations in divergence form with merely bounded and measurable coefficients. AMS subject
openaire +2 more sources
International Journal of Industrial Engineering and Production Research, 2007 : There are some methods for solving integro-differential equations. In this work, we solve the general-order Feredholm integro-differential equations. The Petrov-Galerkin method by considering Chebyshev multiwavelet basis is used.
k. Maleknejad, M. Rabbani
doaj
Discrete & Continuous Dynamical Systems - S, 2011 In this paper we prove some new results concerning a complete abstract second-order differential equation with general Robin boundary conditions. The study is developped in UMD spaces and uses the celebrated Dore-Venni Theorem. We prove existence, uniqueness and maximal regularity of the strict solution.
M. Cheggag +4 more
openaire +3 more sources
Eurasian Mathematical Journal, 2018 Summary: In this paper, we consider regularized solutions for a class of abstract degenerate multi-term fractional differential equations with Caputo derivatives. Our results seem to be new even for non-degenerate differential equations under consideration.
Fedorov, Vladimir Evgen'evich +1 more
openaire +2 more sources
On the Construction of the Trajectory of a Dynamical System with Initial Data on the Hyperplanes
Известия Иркутского государственного университета: Серия "Математика", 2015 In this paper we consider the problems of correct solvability of the initial value problem for a class of differential equations in Banach spaces. We apply the method of reduction of degenerate differential equation to the regular problems using the ...
O.A. Romanova, N.A. Sidorov
doaj
Semigroups on Frechet spaces and equations with infinite delays
, 2007 In this paper, we show existence and uniqueness of a solution to a functional differential equation with infinite delay. We choose an appropriate Frechet space so as to cover a large class of functions to be used as initial functions to obtain existence ...
Sengadir, T
core
Existence and comparison results for operator and differential equations in abstract spaces
Journal of Mathematical Analysis and Applications, 2002 The author proves a fixed-point theorem for increasing mappings \(G:P\to P\) (\(P\) a partially ordered set), together with monotone increasing dependence of selected fixed-points with respect to \(G\). The results are applied to discontinuous implicit functional-differential equations in ordered Banach spaces.
openaire +2 more sources
Some problems in abstract stochastic differential equations on Banach spaces
, 2011 This thesis studies abstract stochastic differential equations on Banach spaces. The well-posedness of abstract stochastic differential equations on such spaces is a recent result of van Neerven, Veraar and Weis, based on the theory of stochastic integration of Banach space valued processes constructed by the same authors.
openaire +2 more sources