Artículos de revistas
Superlinear systems of second-order ODE's
Registro en:
Nonlinear Analysis-theory Methods & Applications. Pergamon-elsevier Science Ltd, v. 68, n. 6, n. 1765, n. 1773, 2008.
0362-546X
WOS:000253882100029
10.1016/j.na.2007.01.001
Autor
Figueiredo, DG
Ubilla, P
Institución
Resumen
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 infinity. 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'''. (c) 2007 Elsevier Ltd. All rights reserved. 68 6 1765 1773