A classical critical point theorem in presence of splitting established by Brézis-Nirenberg is extended to functionals which are the sum of a locally Lipschitz continuous term and of a convex, proper, lower semicontinuous function. The obtained result is then exploited to prove a multiplicity theorem for a family of elliptic variational-hemivariational eigenvalue problems. © 2005 Elsevier Inc. All rights reserved.
Livrea, R., Marano, S., Motreanu, D. (2006). Critical points for nondifferentiable functions in presence of splitting. JOURNAL OF DIFFERENTIAL EQUATIONS, 226(2), 704-725 [10.1016/j.jde.2005.11.001].
Critical points for nondifferentiable functions in presence of splitting
Livrea, R.;Marano, S. A.;Motreanu, D.
2006-01-01
Abstract
A classical critical point theorem in presence of splitting established by Brézis-Nirenberg is extended to functionals which are the sum of a locally Lipschitz continuous term and of a convex, proper, lower semicontinuous function. The obtained result is then exploited to prove a multiplicity theorem for a family of elliptic variational-hemivariational eigenvalue problems. © 2005 Elsevier Inc. All rights reserved.
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