DCDS-B
Preface
Bo Guan Jong-Shenq Guo Bei Hu Urszula Ledzewicz Yuan Lou Fernando Reitich
Discrete & Continuous Dynamical Systems - B 2012, 17(6): i-iii doi: 10.3934/dcdsb.2012.17.6i
It is our great privilege to serve as Guest Editors for this special issue of Discrete and Continuous Dynamical Systems, Series B honoring Professor Avner Friedman on his 80th birthday.

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DCDS-B
A Monge-Ampère type fully nonlinear equation on Hermitian manifolds
Bo Guan Qun Li
Discrete & Continuous Dynamical Systems - B 2012, 17(6): 1991-1999 doi: 10.3934/dcdsb.2012.17.1991
We study a fully nonlinear equation of complex Monge-Ampère type on Hermitian manifolds. We establish the a priori estimates for solutions of the equation up to the second order derivatives with the help of a subsolution.
keywords: a priori estimates. fully nonlinear equations Hermitian manifolds Complex Monge-Ampère equations
DCDS
The Dirichlet problem for Hessian type elliptic equations on Riemannian manifolds
Bo Guan Heming Jiao
Discrete & Continuous Dynamical Systems - A 2016, 36(2): 701-714 doi: 10.3934/dcds.2016.36.701
We apply some new ideas to derive $C^2$ estimates for solutions of a general class of fully nonlinear elliptic equations on Riemannian manifolds under a ``minimal'' set of assumptions which are standard in the literature. Based on these estimates we solve the Dirichlet problem using the continuity method and degree theory.
keywords: concavity. a priori estimates Fully nonlinear elliptic equations on Riemannian manifolds subsolutions Dirichlet problem

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