Minimax Theory and its Applications 01 (2016), No. 1, 125--143
Copyright Heldermann Verlag 2016
Sturm-Liouville Equations Involving Discontinuous Nonlinearities
Gabriele Bonanno
Dept. of Engineering and Applied Mathematics, University of Messina, 98166 Messina, Italy
bonanno@unime.it
Giuseppina D'Aguì
Dept. of Engineering and Applied Mathematics, University of Messina, 98166 Messina, Italy, Italy
dagui@unime.it
Patrick Winkert
Technische Universität Berlin, Institut für Mathematik, Strasse des 17. Juni 136, 10623 Berlin, Germany
winkert@math.tu-berlin.de
This paper deals with equations of Sturm-Liouville-type having nonlinearities on the right-hand side being possibly discontinuous. We present different existence results of such equations under various hypotheses on the nonlinearities. Our approach relies on critical point theory for locally Lipschitz functionals. In particular, under suitable assumptions, an existence result of a non-zero local minimum for locally Lipschitz functionals is established.
Keywords: Discontinuous nonlinearities, Nonsmooth critical point theory, Sturm-Liouville equations, Variational methods.
MSC: 34B15, 34A36
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