Type: Seminar

Distribution: World

Expiry: 11 Aug 2009

Auth: florica@p7192.pc (assumed)

Speaker: Zhaoli Liu from Capital Normal University, Beijing 3:00pm-4:00pm, Monday 10th August, Carslaw 454 Title: Nonlinear elliptic equations and systems with a kind of twisted nonlinearities Abstract: Consider the elliptic equation (E) $ -\Delta u = f(x, u)$ in $\Omega$ with $u=0$ on $\partial \Omega$ and the elliptic system (S) $-\Delta u = \nabla_u V(x, u)$ in $\Omega$ subject to $u=0$ on $\partial\Omega$, where $\Omega$ is a bounded domain in $R^N$ with smooth boundary $\partial\Omega$. Under suitable conditions on $f:\Omega\times R\to R$ and $V:\Omega\times R^m\to R$, nontrivial solutions are obtained for (E) provided that $f(x,t)/t$ crosses several eigenvalues of $-\Delta$. 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.)