Multiplicity results for some classes of non-local elliptic equations

Series: 
CDSNS Colloquium
Monday, January 29, 2018 - 11:15
1 hour (actually 50 minutes)
Location: 
skiles 005
,  
Beijing Normal University
Organizer: 
We will consider the nonlinear elliptic PDEs driven by the fractional Laplacian with superlinear or asymptotically linear terms or combined nonlinearities. An L^infinity regularity result is given using the De Giorgi-Stampacchia iteration method. By the Mountain Pass Theorem and other nonlinear analysis methods, the local and global existence and multiplicity of non-trivial solutions for these equations are established. This is joint work with Yuanhong Wei.