In this paper we deal with the existence and multiplicity of critical points for non differentiable integral functionals defined in the Sobolev space W1,p(Ω) (p > 1) by: 0 where Ω is a bounded open set of RN, with N ≥ 3 and p ≤ N. Under natural assump- tions F turns out to be not Frech ́et differentiable on W1,p(Ω), thus classical critical point theory cannot be applied. The existence of a critical point of F has been proved in [1] by means of a suitable extension of the Ambrosetti-Rabinowitz minimax result. Here we get existence and multiplicity of critical points of F applying a generalization of a symmetric version of the Mountain-Pass theorem proved in [10]. We will follow the same procedure of [7] where the quasilinear case has been treated.
Critical Points for Non Differentiable Functionals
PELLACCI, Benedetta
1997-01-01
Abstract
In this paper we deal with the existence and multiplicity of critical points for non differentiable integral functionals defined in the Sobolev space W1,p(Ω) (p > 1) by: 0 where Ω is a bounded open set of RN, with N ≥ 3 and p ≤ N. Under natural assump- tions F turns out to be not Frech ́et differentiable on W1,p(Ω), thus classical critical point theory cannot be applied. The existence of a critical point of F has been proved in [1] by means of a suitable extension of the Ambrosetti-Rabinowitz minimax result. Here we get existence and multiplicity of critical points of F applying a generalization of a symmetric version of the Mountain-Pass theorem proved in [10]. We will follow the same procedure of [7] where the quasilinear case has been treated.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.