Positive solutions of two-point boundary value problems for second-order differential equations with the nonlinearity dependent on the derivative

摘要

The existence of positive solutions is established for two-point boundary value problems for second-order differential equations with the nonlinearity dependent on the derivative: { (L phi) (x) = h(x) f (phi(x), phi'(x)), 0 <= x <= 1, R-1(phi) alpha(1)phi(0) + beta(1)phi'(0) = 0, R-2(phi) alpha(2)phi(1) + beta(2)phi'(1) = 0, where (L phi)(x) = -(p(x)phi'(x))' + q(x)phi(x). Conditions are given in terms of the relative behaviors of the quotient f(u,v)/vertical bar u vertical bar+vertical bar v vertical bar for vertical bar u vertical bar + vertical bar v vertical bar near 0 and + infinity. (C) 2007 Elsevier Ltd. All rights reserved.