On gamma-convergence for problems of jumping type

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 $alpha,eta$ plays a fundamental role. We prove the existence of at least three critical values for $f_h$, when $alpha$ and $eta$ satisfy the usual assumption with respect to $f_infty$, but not with respect to $f_h$.

Keywords

• $Gamma$-convergence
• jumping problems
• nonsmooth critical point theory.