Abstract
SynopsisIn this paper we study the existence and uniqueness of the two point boundary value problems −(p(x)u′(x))′ = f(x, u(x), u′(x)), xε(0, 1), u′(0)−cu(0) = 0 = u′(1) + du(1), where ∂f/∂u is bounded. above by the least eigenvalue of associated linear problems and ∂f/∂u is bounded. By using monotone techniques to investigate the equivalent problem −(p(x)u′(x))′ + r(x)u(x) = f(x, u(x), u′(x)) + r(x)u(x) where r ε C[0, 1] we show thatgives the optimal bounds for ∂f/∂u and ∂f/u′ when c and d are nonnegative constants.
Publisher
Cambridge University Press (CUP)