Existence of Three Positive Solutions for m-Point Discrete Boundary Value Problems with p-Laplacian. (29th October 2009) - Guo, Yanping; Wei, Wenying; Chen, Yuerong
Abstract : We consider the multi-point discrete boundary value problem with one-dimensionalp -Laplacian operatorΔ ( ϕ p ( Δ u ( t − 1 ) ) + q ( t ) f ( t, u ( t ), Δ u ( t ) ) = 0, t ∈ 1, …, n − 1 subject to the boundary conditions:u ( 0 ) = 0, u ( n ) = ∑ i = 1 m − 2 a i u ( ξ i ), whereϕ p ( s ) = | s | p − 2 s, p > 1, ξ i ∈ 2, …, n − 2 with1 < ξ 1 < ⋯ < ξ m − 2 < n − 1 anda i ∈ ( 0, 1 ), 0 < ∑ i = 1 m − 2 a i < 1 . Using a new fixed point theorem due to Avery and Peterson, we study the existence of at least three positive solutions to the above boundary value problem.