ftp ejde.math.txstate.edu (login: ftp) EXISTENCE AND UNIQUENESS OF POSITIVE SOLUTIONS FOR A BVP WITH A P-LAPLACIAN ON THE HALF-LINE

Abstract. In this work, we consider the second order multi-point boundary-value problem with a p-Laplacian (ρ(t)Φp(x ′(t))) ′ + f(t, x(t), x′(t)) = 0, t ∈ [0,+∞), x(0) = mX i=1 αix(ξi), lim t→∞x(t) = 0. By applying a nonlinear alternative theorem, we establish existence and unique-ness of solutions on the half-line. Also a uniqueness result for positive solutions is discussed when f depends on the first-order derivative. The emphasis here is on the one dimensional p-Laplacian operator. 1