Electronic Journal of Differential Equations,
Vol. 2003(2003), No. 60, pp. 1-16.
Title: On $\Gamma$-convergence for problems of jumping type
Author: Alessandro Groli (University of Brescia, Italy)
Abstract:
The convergence of critical values for a sequence of functionals
$(f_h)$ $\Gamma$-converging to a functional $f_{\infty}$ is studied.
These functionals are related to a classical ``jumping problem'',
in which the position of two real parameters $\alpha,\beta$ plays
a fundamental role.
We prove the existence of at least three critical values
for $f_h$, when $\alpha$ and $\beta$ satisfy the usual assumption
with respect to $f_\infty$, but not with respect to $f_h$.
Submitted February 19, 2003. Published May 23, 2003.
Math Subject Classifications: 49J45, 58E05.
Key Words: $\Gamma$-convergence; jumping problems;
nonsmooth critical point theory.