Existence and topological structure of solution sets for φ-Laplacian impulsive stochastic differential systems

Tayeb Blouhi, Mohamed Ferhat

Abstract


In this article, we present results on the existence and the topological struc-
ture of the solution set for initial-value problems for the rst-order impulsive
dierential equation with innite Brownian motions are proved.The approach is
based nonlinear alternative Leary-Schauder type theorem in generalized Banach
spaces


Keywords


-Laplacian Stochastic dierential equation, Wiener process, impulsive dierential equations, Matrix convergent to zero, Generalized Banach space, Fixed point.

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References


A. T. Bharucha-Reid, Random Integral Equations, Academic Press, New York,

......................................................................................

A. Viorel, Contributions to the Study of Nonlinear Evolution Equations, Ph.D.

...................................................................

thesis, Babes-Bolyai University Cluj-Napoca Department of Mathematics, 2011.

................................................................

A. Halanay and D. Wexler, Teoria Calitativa a sistemelor Impulsuri, (in Romanian),

.......................................................................

Editura Academiei Republicii Socialiste Rom^ania, Bucharest, 1968.

A. A. Novikov, The moment inequalities for stochastic integrals. (Russian) Teor.

..........................................................

Verojatnost. i Primenen., 16 (1971) 548-551.

A.M. Samoilenko and N.A. Perestyuk, Impulsive Dierential Equations, World

Scientic, Singapore, 1995.

......................................................................

A.I. Perov, On the Cauchy problem for a system of ordinary dierential equations,

Pviblizhen. Met. Reshen

......................................

Dier. Uvavn., 2, (1964), 115-134. (in Russian).

B. Davis, On the integrability of the martingale square function, Israel J. Math.

(1970) 187-190.

...............................................................................

B. ksendal, Stochastic Dierential Equations:An Introduction with Applications

(Fourth Edition) Springer-Verlag, Berlin, 1995.

................................................................................

C. Guilan and H. Kai, On a type of stochastic dierential equations driven by




DOI: http://dx.doi.org/10.24193/subbmath.2018.4.07

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