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Liu Bie Ju Centre for Mathematical Sciences
City University of Hong Kong
Mathematical Analysis and its Applications
Colloquium

Organized by Prof. Philippe G. Ciarlet and Prof. Roderick Wong

The Uniqueness Problem of the Ground State of Emden Fowler Equations

by
Professor Man Kam Kwong
Lucent Technologies Inc.

Date: December 15, 2004 (Wednesday)
Time: 4:30 pm to 5:30 pm
Venue: Room B6605 (Faculty Conference Room)
Blue Zone, Level 6
Academic Building
City University of Hong Kong

Abstract: Many interesting physical problems lead to n-dimensional second-order semi-linear elliptic equations of the form Δu + f(u) = 0 with various (sufficiently smooth) functions f(u). The particular example f(u) = u^p - u (where p is a positive constant) has appeared in the study of many unrelated physical phenomena. A solution of the equation in a given region (which can be bounded or unbounded) is said to be a ground state solution if it is positive in the interior of the region, and zero on the boundary of the region (and/or approaches zero as x→¥ if the region is unbounded). It is a well-known result of Gidas, Ni, and Nirenberg that if the region is a ball or (if f(u) is sufficiently nice) the entire Rⁿ, then the solution must be radially symmetric. In this situation, the solution u(r) satisfies the generalized Emden-Fowler differential equation

A natural question (and it turns out to be a very useful one) to ask is whether the ground state is unique or not. In this talk we survey some known results, techniques of proof, and open problems concerning this question.

(Tea, coffee and cookies will be provided at the Faculty Common Room in B6501 before the colloquium from 4:00 to 4:30 pm. Please come and join us!)

** All interested are welcome **

For enquiry: 2788-9816

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