Electron. J. Diff. Eqns., Vol. 2003(2003), No. 60, pp. 1-16.

On $\Gamma$-convergence for problems of jumping type

Alessandro Groli

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.

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Alessandro Groli
Department of Mathematics
University of Brescia
Via Valotti 9, 25133 Brescia, Italy
email: alessandro.groli@ing.unibs.it

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