Abstract
This paper deals with the existence of positive solutions for the one-dimensional p -Laplacian ( ϕ p ( u ′ ) ) ′ + f ( t , u , u ′ ) = 0 , t ∈ [ 0 , 1 ] , subject to the boundary value conditions: u ′ ( 0 ) = ∑ i = 1 n α i u ′ ( ξ i ) , u ( 1 ) = ∑ i = 1 n β i u ( ξ i ) , where ϕ p ( s ) = | s | p − 2 s , p > 1 . We show that it has at least one or two positive solutions under some assumptions by applying the fixed point theorem. The interesting points are that the nonlinear term f is involved with the first-order derivative explicitly and f may change sign.
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