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.
- 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...
- Almost Periodic Solutions of Differential Equations in Banach Spaces: Some New Results and Methods. Naito, Toshiki; Van Minh, Nguyen; Jong Son Shin // Vietnam Journal of Mathematics;Dec2001, Vol. 29 Issue 4, p295
Presents the periodic solutions of differential equations and functional differential equations in Banach spaces. Assumption that Banach spaces generate a strongly continuous periodic evolutionary process; Spectral properties of either the operator-coefficients in the case of autonomous...
- 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 ? (0; 1) with the internal nonlocal condition Smk=1 akx(_k) = xo; ?_k ? (c; d) ? (0; 1): The problem of the integral condition...
- 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...
- A Note on A Paper of Cellina Concerning Differential Equations in Banach Spaces. Kunze, M. // Bulletin of the London Mathematical Society;1996, Vol. 28 Issue 6, p613
The article investigates the differential equations in Banach spaces with a right-hand side being more general than Lipschitz. It provides a detailed understanding on the proof of an existence theorem under the additional assumption that the right-hand side is uniformly continuous. It also...
- Smoothing properties of transition semigroups relative to SDEs with values in Banach spaces. Cerrai, Sandra // Probability Theory & Related Fields;1999, Vol. 113 Issue 1, p85
Abstract. In the present paper we consider the transition semigroup P[sub t] related to some stochastic reaction-diffusion equations with the nonlinear term f having polynomial growth and satisfying some dissipativity conditions. We are proving that it has a regularizing effect in the Banach...
- Weakly almost periodic solutions for some differential... Dads, E. Ait; Ezzinbi, K.; Fatajou, S. // Nonlinear Studies;1997, Vol. 4 Issue 2, p157
Presents the derivation for weakly almost periodic functions with a Banach space. Applications of the results to investigate the weakly periodic solutions of some differential equations in a Banach space; Notations and basic properties of wap functions; Solution of ordinary differential equations.