Artículos de revistas
Superlinear systems of second-order ODE's
Nonlinear Analysis-theory Methods & Applications. Pergamon-elsevier Science Ltd, v. 68, n. 6, n. 1765, n. 1773, 2008.
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.68617651773