We consider the semilinear eigenvalue problem
where p > 1 is a constant, and is a parameter. We propose a new inverse bifurcation problem. Assume that k(t) is an unknown function. Then can we determine k(t) from the asymptotic behavior of the bifurcation curve? The purpose of this paper is to answer this question affirmatively. The key ingredient is the precise asymptotic formula for the -bifurcation curve as ( ), where .
Submitted December 28, 2012. Published May 10, 2013.
Math Subject Classifications: 34C23, 34B15.
Key Words: Inverse bifurcation problem; non-autonomous equation; logistic equations.
Show me the PDF file (269 KB), TEX file, and other files for this article.
| Tetsutaro Shibata |
Laboratory of Mathematics, Institute of Engineering
Hiroshima University, Higashi-Hiroshima, 739-8527, Japan
Return to the EJDE web page