Linear approximation of nonlinear Schrödinger equations driven by cylindrical Wiener processes

Wilfried  Grecksch; Hannelore  Lisei

doi:10.3934/dcdsb.2016089

Article Contents

2016, Volume 21, Issue 9: 3095-3114. Doi: 10.3934/dcdsb.2016089

This issue Previous Article Semilinear stochastic equations with bilinear fractional noise Next Article Taylor schemes for rough differential equations and fractional diffusions

Linear approximation of nonlinear Schrödinger equations driven by cylindrical Wiener processes

Wilfried Grecksch^1, and
Hannelore Lisei^2,

1.
Martin-Luther-University Halle-Wittenberg, Faculty of Natural Sciences II, Institute of Mathematics, 06099 Halle (Saale)
2.
Babeş-Bolyai University, Faculty of Mathematics and Computer Science, Str. Kogălniceanu nr. 1, RO - 400084 Cluj-Napoca

Received: November 30, 2015

Revised: January 31, 2016

Published: October 2016

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Abstract

In this paper the existence and uniqueness of the solution for a stochastic nonlinear Schrödinger equation, which is perturbed by a cylindrical Wiener process is investigated. The existence of the variational solution and of the generalized weak solution are proved by using sequences of successive approximations, which are the solutions of certain linear problems.

Keywords:

Nonlinear stochastic Schrödinger equations,
fixed point,
cylindrical Wiener process.

Mathematics Subject Classification: Primary: 60H15, 60H35, 35Q41; Secondary: 81Q05.

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