In this work we obtain some existence results for a class of elliptic Dirichlet problems involving the critical Sobolev exponent and containing a parameter. Through a weak lower semicontinuity result and by using a critical point theorem for differentiable functionals, the existence of a precise open interval of positive eigenvalues for which the treated problems admit at least one non-trivial weak solution is established. The attained results represent a more precise version of some contributions on the treateIn this work we obtain some existence results for a class of elliptic Dirichlet problems involving the critical Sobolev exponent and containing a parameter. Through a weak lower semicontinuity result and by using a critical point theorem for differentiable functionals, the existence of a precise open interval of positive eigenvalues for which the treated problems admit at least one non-trivial weak solution is established. The attained results represent a more precise version of some contributions on the treated subject.

A note on elliptic equations involving the critical Sobolev exponent

Molica Bisci G
;
2013-01-01

Abstract

In this work we obtain some existence results for a class of elliptic Dirichlet problems involving the critical Sobolev exponent and containing a parameter. Through a weak lower semicontinuity result and by using a critical point theorem for differentiable functionals, the existence of a precise open interval of positive eigenvalues for which the treated problems admit at least one non-trivial weak solution is established. The attained results represent a more precise version of some contributions on the treateIn this work we obtain some existence results for a class of elliptic Dirichlet problems involving the critical Sobolev exponent and containing a parameter. Through a weak lower semicontinuity result and by using a critical point theorem for differentiable functionals, the existence of a precise open interval of positive eigenvalues for which the treated problems admit at least one non-trivial weak solution is established. The attained results represent a more precise version of some contributions on the treated subject.
File in questo prodotto:
Non ci sono file associati a questo prodotto.

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11576/2664255
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 0
  • ???jsp.display-item.citation.isi??? 0
social impact