PDE Seminar (2016/5/13): Two positive solutions for the Kirchhoff type elliptic problem with critical nonlinearity in high dimension, Daisuke Naimen (Muroran Institute of Technology)

2016-5-13 16:30 - 2016-5-13 18:00
Faculty of Science Building #3, Room 309
Daisuke Naimen (Muroran Institute of Technology)
Recently, the stationary problem of the Kirtchhoff type wave equation is extensively investigated. In this talk, we discuss our recent studies on such a Kirchhoff type elliptic problem involving the critical Sobolev exponent. Because of the interaction between the critical nonlinearity and the Kirchhoff type nonlocal dependence, serious difficulties occur in proving the existence of solutions. Overcoming such difficulties, we get new multiplicity results. We mainly show our idea to deal with the problem in high dimension. Our method is based on the variational method and the concentration compactness analysis on Palais-Smale sequences.