Abstract :
This paper deals with the existence of multiple positive solutions for the one-dimensional p-
Laplacian
ϕp x (t ) +q(t)f t,x(t),x (t ) = 0, t∈ (0, 1),
subject to one of the following boundary conditions:
αϕp x(0) − βϕp x (0) = 0, γϕp x(1) + δϕp x (1) = 0,
or
x(0) −g1 x (0) = 0, x(1) + g2 x (1) = 0,
where ϕp(s) = |s|p−2 s, p > 1. By means of a fixed point theorem due to Avery and Peterson,
sufficient conditions are obtained that guarantee the existence of at least three positive solutions. The
interesting point is the nonlinear term f is involved with the first-order derivative explicitly.
2004 Elsevier Inc. All rights reserved.
