Superlinear systems of second-order ODE's

Figueiredo, DG; Ubilla P.

Abstract

We discuss the existence of positive solutions of the system - u″ = f (t, u, v, u′, v′) in (0, 1),- v″ = g (t, u, v, u′, v′) in (0, 1),u (0) = u (1) = v (0) = v (1) = 0 where the nonlinearities f and g satisfy a superlinearity condition at both 0 and ∞. Our main result is the proof of a priori bounds for the eventual solutions. As an application, we consider the Dirichlet problem in an annulus for systems of semilinear elliptic equations with nonlinearities depending on the gradient as well. As a second application, we consider fourth-order elastic beam equations with dependence also on the derivatives u′, u″, u‴. © 2007 Elsevier Ltd. All rights reserved.

Más información

Título según WOS: Superlinear systems of second-order ODE's
Título según SCOPUS: Superlinear systems of second-order ODE's
Título de la Revista: NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS
Volumen: 68
Número: 6
Editorial: PERGAMON-ELSEVIER SCIENCE LTD
Fecha de publicación: 2008
Página de inicio: 1765
Página final: 1773
Idioma: English
URL: http://linkinghub.elsevier.com/retrieve/pii/S0362546X07000363
DOI:

10.1016/j.na.2007.01.001

Notas: ISI, SCOPUS