Existence of three positive solutions for -point boundary-value problems with one-dimensional -Laplacian

✍ Scribed by Hanying Feng; Weigao Ge

• Publisher: Elsevier Science
• Year: 2008
• Tongue: English
• Weight: 214 KB
• Volume: 68
• Category: Article
• ISSN: 0362-546X
• DOI: 10.1016/j.na.2007.01.029

✦ Synopsis

In this paper, we consider the multipoint boundary value problem for the one-dimensional p-Laplacian (φ p (u )) + q(t) f (t, u(t), u (t)) = 0, t ∈ (0, 1), subject to the boundary conditions:

where φ p (s) = |s| p-2 s, p > 1, ξ i ∈ (0, 1) with 0 < ξ 1 < ξ 2 < • • • < ξ m-2 < 1 and a i ∈ [0, 1), 0 ≤ m-2 i=1 a i < 1. Using a fixed point theorem due to Avery and Peterson, we study the existence of at least three positive solutions to the above boundary value problem. The interesting point is that the nonlinear term f explicitly involves a first-order derivative.