The paper deals with the boundary value problem on the whole line (P): u''-f(u,u')+g(u)=0, u(-∞)=0, u(+∞)=1, where g:R →R is a continuous non-negative function with support [0,1] and f:R^2 →R is a continuous function. By means of a new approach, based on a combination of lower and upper-solutions methods and phase-plane techniques, we prove an existence result for (P) when f is superlinear in u'; by a similar technique, we also get a non-existence one. As an application, we investigate the attractivity of the singular point (0,0) in the phase-plane (u,u'). We refer to a forthcoming paper for a further application in the field of front-type solutions for reaction-diffusion equations

Existence of bounded trajectories via upper and lower solutions / Malaguti, L.; Marcelli, Cristina. - In: DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS. - ISSN 1078-0947. - STAMPA. - 6:3(2000), pp. 575-590.

Existence of bounded trajectories via upper and lower solutions

MARCELLI, Cristina
2000-01-01

Abstract

The paper deals with the boundary value problem on the whole line (P): u''-f(u,u')+g(u)=0, u(-∞)=0, u(+∞)=1, where g:R →R is a continuous non-negative function with support [0,1] and f:R^2 →R is a continuous function. By means of a new approach, based on a combination of lower and upper-solutions methods and phase-plane techniques, we prove an existence result for (P) when f is superlinear in u'; by a similar technique, we also get a non-existence one. As an application, we investigate the attractivity of the singular point (0,0) in the phase-plane (u,u'). We refer to a forthcoming paper for a further application in the field of front-type solutions for reaction-diffusion equations
2000
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/11566/29698
 Attenzione

Attenzione! I dati visualizzati non sono stati sottoposti a validazione da parte dell'ateneo

Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 10
  • ???jsp.display-item.citation.isi??? 10
social impact