Existence and compactness for weak solutions to bellman systems with critical growth

Alain Bensoussan; Miroslav Bulíĉek; Jens Frehse

doi:10.3934/dcdsb.2012.17.1729

Author(s)

Alain Bensoussan
Miroslav Bulíĉek
Jens Frehse

Detail(s)

Original language	English
Pages (from-to)	1729-1750
Journal / Publication	Discrete and Continuous Dynamical Systems - Series B
Volume	17
Issue number	6
Publication status	Published - 2012
Externally published	Yes

Link(s)

DOI	DOI https://doi.org/10.3934/dcdsb.2012.17.1729 Final Published version
	Check@CityULib
Link to Scopus	https://www.scopus.com/record/display.uri?eid=2-s2.0-84870749083&origin=recordpage
Permanent Link	https://scholars.cityu.edu.hk/en/publications/publication(05cfbf5f-3a9d-4751-8a45-6fc9f8faf348).html

Abstract

We deal with nonlinear elliptic and parabolic systems that are the Bellman systems associated to stochastic differential games as a main motivation. We establish the existence of weak solutions in any dimension for an arbitrary number of equations (\players"). The method is based on using a renormalized sub- and super-solution technique. The main novelty consists in the new structure conditions on the critical growth terms with allow us to show weak solvability for Bellman systems to certain classes of stochastic differential games.

Citation Format(s)

[ RIS ] [ BibTeX ]

Existence and compactness for weak solutions to bellman systems with critical growth. / Bensoussan, Alain; Bulíĉek, Miroslav; Frehse, Jens.
In: Discrete and Continuous Dynamical Systems - Series B, Vol. 17, No. 6, 2012, p. 1729-1750.

Research output: Journal Publications and Reviews › RGC 21 - Publication in refereed journal › peer-review

Bensoussan, A, Bulíĉek, M & Frehse, J 2012, 'Existence and compactness for weak solutions to bellman systems with critical growth', Discrete and Continuous Dynamical Systems - Series B, vol. 17, no. 6, pp. 1729-1750. https://doi.org/10.3934/dcdsb.2012.17.1729

Bensoussan, A., Bulíĉek, M., & Frehse, J. (2012). Existence and compactness for weak solutions to bellman systems with critical growth. Discrete and Continuous Dynamical Systems - Series B, 17(6), 1729-1750. https://doi.org/10.3934/dcdsb.2012.17.1729

Bensoussan A, Bulíĉek M, Frehse J. Existence and compactness for weak solutions to bellman systems with critical growth. Discrete and Continuous Dynamical Systems - Series B. 2012;17(6):1729-1750. doi: 10.3934/dcdsb.2012.17.1729

Bensoussan, Alain ; Bulíĉek, Miroslav ; Frehse, Jens. / Existence and compactness for weak solutions to bellman systems with critical growth. In: Discrete and Continuous Dynamical Systems - Series B. 2012 ; Vol. 17, No. 6. pp. 1729-1750.