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Multisummability and ordinary meromorphic differential equations

Boele Braaksma (2012)

Banach Center Publications

In this expository paper we consider various approaches to multisummability. We apply it to nonlinear ODE's and give a somewhat modified proof of multisummability of formal solutions of ODE's with levels 1 and 2 via Écalle's method involving convolution equations.

Multi-type synchronization of impulsive coupled oscillators via topology degree

Yingjie Bi, Zhidan Cai, Shuai Wang (2024)

Applications of Mathematics

The existence of synchronization is an important issue in complex dynamical networks. In this paper, we study the synchronization of impulsive coupled oscillator networks with the aid of rotating periodic solutions of impulsive system. The type of synchronization is closely related to the rotating matrix, which gives an insight for finding various types of synchronization in a united way. We transform the synchronization of impulsive coupled oscillators into the existence of rotating periodic solutions...

Multivalued backward stochastic differential equations with time delayed generators

Bakarime Diomande, Lucian Maticiuc (2014)

Open Mathematics

Our aim is to study the following new type of multivalued backward stochastic differential equation: - d Y t + φ Y t d t F t , Y t , Z t , Y t , Z t d t + Z t d W t , 0 t T , Y T = ξ , where ∂φ is the subdifferential of a convex function and (Y t, Z t):= (Y(t + θ), Z(t + θ))θ∈[−T,0] represent the past values of the solution over the interval [0, t]. Our results are based on the existence theorem from Delong Imkeller, Ann. Appl. Probab., 2010, concerning backward stochastic differential equations with time delayed generators.

Multivalued linear operators and differential inclusions in Banach spaces

Anatolii Baskakov, Valeri Obukhovskii, Pietro Zecca (2003)

Discussiones Mathematicae, Differential Inclusions, Control and Optimization

In this paper, we study multivalued linear operators (MLO's) and their resolvents in non reflexive Banach spaces, introducing a new condition of a minimal growth at infinity, more general than the Hille-Yosida condition. Then we describe the generalized semigroups induced by MLO's. We present a criterion for an MLO to be a generator of a generalized semigroup in an arbitrary Banach space. Finally, we obtain some existence results for differential inclusions with MLO's and various types of multivalued...

Multi-valued operators and fixed point theorems in Banach algebras

Bapur Chandra Dhage (2004)

Discussiones Mathematicae, Differential Inclusions, Control and Optimization

In this paper, two multi-valued versions of the well-known hybrid fixed point theorem of Dhage [6] in Banach algebras are proved. As an application, an existence theorem for a certain differential inclusion in Banach algebras is also proved under the mixed Lipschitz and compactness type conditions.

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