| Abstract: |
| We consider the asymptotic behavior of
bifurcation curves for semilinear eigenvalue problems
with some oscillatory nonlinear terms.
We treat the case where $\lambda$ is
parameterized by
the maximum norm $\alpha = \Vert u_\lambda\Vert_\infty$ of the solution
$u_\lambda$
associated with $\lambda$. Then $\lambda$ is
represented as $\lambda = \lambda(\alpha)$.
In this talk, we focus on the problems
where $\lambda(\alpha) \to \pi^2/4$
as $\alpha \to \infty$.
We establish the asymptotic formulas
for $\lambda(\alpha)$ as $\alpha \to \infty$
and $\alpha \to 0$
with the exact second terms. Then we understand well the whole structures
of the bifurcation curves. |
|