演講公告

演講主題：Extensions of bifurcation from simple eigenvalue theorem
主講人：Prof. Junping Shi (清華大學訪問教授)
演講日期：96年11月27日(星期二)<br>下午2:30 – 3:20
演講地點：(光復校區)科學一館223室
茶會時間：當天下午2:00科學一館205室
摘要內容：
Nonlinear equations can often be formulated as a nonlinear operator equation in Banach spaces, and the linearized operators are often linear Fredholm operators of index zero. Examples include a large class of quasilinear elliptic systems with nonlinear boundary conditions. A classical theorem of Crandall and Rabinowitz states that a bifurcation occurs at a simple eigenvalue along a branch of trivial solutions, and near the bifurcation point, the solution set consists of a line segment and a curve crossing it. We show a bifurcation theorem generalizing the classical one without a priori knowledge of a line of trivial solutions, which can also be used in perturbation problem of degenerate solutions. In another extension we show that the bifurcation from a simple eigenvalue is indeed global, which is also an extension of Rabinowitz's global bifurcation theorem which requires compactness.

$返回$ go back