Multiplicity of positive and nodal solutions for scalar field equations

TitleMultiplicity of positive and nodal solutions for scalar field equations

 

Speaker Prof. Giovanna Cerami (Polytechnical University of Bari

 

Time 16:00-17:00 pm, September 18, 2014

 

Venue Conference Room A404, Department of Mathematical Sciences

 

AbstractThe question of finding infinitely many changing sign solutions to the problem −?u+a(x)u = |u|^{p−1}u, in R^N, u H^1(R^N), is considered when N 2, p 1, p < 2N/(N − 2))  if N 3, and the potential a(x) is a positive function, which approaches its limit at infinity from above and which is not required to enjoy symmetry properties. 

      Assuming that a(x) satisfies a suitable “slow decay at infinity” condition and, more- over, that its graph has some “dips”, the existence of infinitely many nodal solutions will be shown by using a variational method.

 

ContactWenming Zou