In this paper we study general functionals of the calculus of variations with the presence of a Hardy potential. We will improve several results obtained in the semilinear framework. We will first prove a general weak lower semicontinuity result, which will imply the existence of a minimum point whenever the functional is coercive. Then we will demonstrate existence and multiplicity results of critical points, even if our functional is not differentiable. We will apply a nonsmooth critical point theory developed in Corvellec et al. (Nonlinear Anal. 1 (1993) 151) and Degiovanni and Marzocchi (Ann. Mat. Pura Appl. 167 (1994) 73).

Multiple critical points for nondifferentiable functionals involving Hardy potentials

PELLACCI, Benedetta
2005-01-01

Abstract

In this paper we study general functionals of the calculus of variations with the presence of a Hardy potential. We will improve several results obtained in the semilinear framework. We will first prove a general weak lower semicontinuity result, which will imply the existence of a minimum point whenever the functional is coercive. Then we will demonstrate existence and multiplicity results of critical points, even if our functional is not differentiable. We will apply a nonsmooth critical point theory developed in Corvellec et al. (Nonlinear Anal. 1 (1993) 151) and Degiovanni and Marzocchi (Ann. Mat. Pura Appl. 167 (1994) 73).
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11367/18609
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