We discuss existence, non-existence and multiplicity of positive solutions of the Dirichlet problem for the one-dimensional prescribed curvature equation $$ -\left({u'}/{\sqrt{1+{u'}{^2}}}\right)'=f(t,u), u(0)=0, u(1)=0, $$ in connection with the changes of concavity of the function $f$. The proofs are based on an upper and lower solution method, we specifically develop for this problem, combined with a careful analysis of the time-map associated with some related autonomous equations.

Multiple positive solutions of a one-dimensional prescribed mean curvature problem

OMARI, PIERPAOLO
2007-01-01

Abstract

We discuss existence, non-existence and multiplicity of positive solutions of the Dirichlet problem for the one-dimensional prescribed curvature equation $$ -\left({u'}/{\sqrt{1+{u'}{^2}}}\right)'=f(t,u), u(0)=0, u(1)=0, $$ in connection with the changes of concavity of the function $f$. The proofs are based on an upper and lower solution method, we specifically develop for this problem, combined with a careful analysis of the time-map associated with some related autonomous equations.
File in questo prodotto:
Non ci sono file associati a questo prodotto.
Pubblicazioni consigliate

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/11368/1697221
 Avviso

Registrazione in corso di verifica.
La registrazione di questo prodotto non è ancora stata validata in ArTS.

Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 59
  • ???jsp.display-item.citation.isi??? 60
social impact