PDE Seminar Abstracts

Nonlinear elliptic equations and systems with a kind of twisted nonlinearities

Zhaoli Liu
Capital Normal University, Beijing
10 Aug 2009 3-4pm, Carslaw Room 454


Consider the elliptic equation (E) - Δu = f(x,u) in Ω with u = 0 on Ω and the elliptic system (S) - Δu = uV (x,u) in Ω subject to u = 0 on Ω, where Ω is a bounded domain in RN with smooth boundary Ω. Under suitable conditions on f : Ω × R R and V : Ω × Rm R, nontrivial solutions are obtained for (E) provided that f(x,t)t crosses several eigenvalues of - Δ. Similar results are proved for (S) as well as for Hamiltonian systems. Here we do not need f(x,t)t to have an asymptotic limit, which was assumed in the literature for similar problems. (This is joint work with Jiabao Su and Zhi-Qiang Wang.)