On the well-posedness of differential equations unsolved for the derivative
- A NOTE ON SOME CAUCHY PROBLEMS WITH NONLOCAL CONDITIONS. N'Guérékata, Gaston M. // Communications in Mathematical Analysis;2008, Vol. 4 Issue 1, p78
In this short note we prove the existence and uniqueness of solutions to semilinear differential equations with nonlocal conditions in a Banach space, first in the case of a nondensely defined operator and second in intermediate Banach spaces. In both cases, we use the contraction mapping principle.
- A simple counterexample related to the Lie-Trotter product formula. Canzi, Claudia; Guerra, Graziano // Semigroup Forum;Jun2012, Vol. 84 Issue 3, p499
In this note a very simple example is given which shows that if the sum of two semigroup generators is itself a generator, the generated semigroup in general can not be given by the Lie-Trotter product formula.
- Global existence and stability for second order functional evolution equations with infinite delay. Baliki, Abdessalam; Benchohra, Mouffak; Graef, John R. // Electronic Journal of Qualitative Theory of Differential Equatio;2016, Issue 1-122, p1
In this article, the authors give sufficient conditions for existence and attractivity of mild solutions for second order semi-linear functional evolution equation in Banach spaces using Schauder's fixed point theorem. An example is provided to illustrate the result.
- On the existence of periodic solutions to higher dimensional periodic system with delay. Xiankai, Huang; Qinxi, Dong // Applied Mathematics & Mechanics;Aug1999, Vol. 20 Issue 8, p908
In this paper, higher dimensional periodic systems with delay of the form are considered. Using the coincidence degree method, some sufficient conditions to guarantee the existence of periodic solution for these systems are obtained. As an application of the results, the existence of a positive...
- Implicit Approximation Scheme for the Solution of K-Positive Definite Operator Equation. Shahzad, Naseer; Rafiq, Arif; Zegeye, Habtu // Abstract & Applied Analysis;2014, p1
We construct an implicit sequence suitable for the approximation of solutions of K-positive definite operator equations in real Banach spaces. Furthermore, implicit error estimate is obtained and the convergence is shown to be faster in comparsion to the explicit error estimate obtained by...
- ON THE REGULARITY OF MILD SOLUTIONS TO COMPLETE HIGHER ORDER DIFFERENTIAL EQUATIONS ON BANACH SPACES. Iraniparast, Nezam; Nguyen, Lan // Surveys in Mathematics & its Applications;2015, Vol. 10, p23
For the complete higher order differential equation u(n)(t) = Î£n-1k=0Aku(k)(t)+f(t), t Îµ R (*) on a Banach space E, we give a new definition of mild solutions of (*). We then characterize the regular admissibility of a translation invariant subspace M of BUC(R,E) with respect to (*) in...
- Amcor Limited SWOT Analysis. // Amcor Limited SWOT Analysis;10/ 1/2014, p1
A SWOT analysis of Amcor Limited is presented.
- On the existence of solutions for a class of fractional differential equations. JinRong Wang; XiWang Dong; Wei Wei // Studia Universitatis Babes-Bolyai, Mathematica;2012, Vol. 57 Issue 1, p15
In this paper, we study the existence and uniqueness of solutions to the Cauchy problem for nonautonomous fractional differential equations involving Caputo derivative in Banach spaces. Definition for the solution in the Carathï¿½odory sense and fundamental lemma are introduced. Some...
- INTERNAL NONLOCAL AND INTEGRAL CONDITION PROBLEMS OF THE DIFFERENTIAL EQUATION x'= f(t, x, x'). El-Sayed, A. M. A.; Hamdallah, E. M.; Elkadeky, Kh. W. // Journal of Nonlinear Sciences & its Applications;2011, Vol. 4 Issue 3, p193
In this work, we are concerned with the existence of at least one absolutely continuous solution of the Cauchy problem for the differential equation x' = f(t; x; x'); t âˆˆ (0; 1) with the internal nonlocal condition Î£mk=1 akx(_k) = xo; Î¤_k âˆˆ (c; d) âŠ‚ (0; 1): The problem of...