Multiplicity results for some classes of non-local elliptic equations

CDSNS Colloquium
Monday, January 29, 2018 - 11:15
1 hour (actually 50 minutes)
skiles 005
Beijing Normal University
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.