DCDS
Positive solutions for non local elliptic problems
Jinggang Tan
Discrete & Continuous Dynamical Systems - A 2013, 33(2): 837-859 doi: 10.3934/dcds.2013.33.837
We establish existence and regularity results, as well as a priori estimates of Gidas-Spruck type for nonlinear problems involving the fractional power of the Dirichlet Laplacian.
keywords: critical exponent Fractional Laplacian nonlinear mixed boundary problem nonlinear Liouville theorems moving planes method. a priori estimates
DCDS
The existence of nontrivial solutions to Chern-Simons-Schrödinger systems
Youyan Wan Jinggang Tan
Discrete & Continuous Dynamical Systems - A 2017, 37(5): 2765-2786 doi: 10.3934/dcds.2017119

We show the existence of nontrivial solutions to Chern-Simons-Schrödinger systems by using the concentration compactness principle and the argument of global compactness.

keywords: Chern-Simons gauge field Schrödinger equation variational methods
DCDS
A Harnack inequality for fractional Laplace equations with lower order terms
Jinggang Tan Jingang Xiong
Discrete & Continuous Dynamical Systems - A 2011, 31(3): 975-983 doi: 10.3934/dcds.2011.31.975
We establish a Harnack inequality of fractional Laplace equations without imposing sign condition on the coefficient of zero order term via the Moser's iteration and John-Nirenberg inequality.
keywords: Harnack inequality Moser's iteration. Fractional Laplace equations

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