In this paper we deal with a bifurcation result for the following Dirichlet problem[ left{egin{array}{ll}-Delta_pu= rac{mu}{|x|^p}|u|^{p-2}u+lambda f(x,u)qquad extrm{ a. e. in }Omega\u_{|partialOmega}=0end{array} ight.]Starting from a weak lower semicontinuity result by E. Montefusco, that allows us to apply a general variational principle by B.Ricceri, we prove that, for $mu$ close to zero, there exists apositive number $lambda^*_mu$ such that, for every $lambdain]0,lambda^*_mu[$ the above problem admits a non-zero weaksolution $u_lambda$ in $W_0^{1,p}(Omega)$ satisfying$lim_{lambda o 0^+}|u_lambda|=0$.

Bifurcations theorems for nonlinear problems with lack of compactness

FARACI, FRANCESCA;
2003-01-01

Abstract

In this paper we deal with a bifurcation result for the following Dirichlet problem[ left{egin{array}{ll}-Delta_pu= rac{mu}{|x|^p}|u|^{p-2}u+lambda f(x,u)qquad extrm{ a. e. in }Omega\u_{|partialOmega}=0end{array} ight.]Starting from a weak lower semicontinuity result by E. Montefusco, that allows us to apply a general variational principle by B.Ricceri, we prove that, for $mu$ close to zero, there exists apositive number $lambda^*_mu$ such that, for every $lambdain]0,lambda^*_mu[$ the above problem admits a non-zero weaksolution $u_lambda$ in $W_0^{1,p}(Omega)$ satisfying$lim_{lambda o 0^+}|u_lambda|=0$.
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/20.500.11769/4781
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus ND
  • ???jsp.display-item.citation.isi??? ND
social impact