We consider the inverse nonlinear eigenvalue problem for the equation
where is an unknown nonlinear term, is a bounded domain with an appropriate smooth boundary and is a parameter. Under basic conditions on , for any given , there exists a unique solution with . The curve is called the -bifurcation branch. Using a variational approach, we show that the nonlinear term is determined uniquely by .
Submitted November 14, 2008. Published September 10, 2009.
Math Subject Classifications: 35P30.
Key Words: Inverse eigenvalue problems; nonlinear elliptic equation; variational method.
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| Tetsutaro Shibata |
Department of Applied Mathematics
Graduate School of Engineering
Hiroshima University, Higashi-Hiroshima, 739-8527, Japan
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