EXISTENCE OF THREE POSITIVE SOLUTIONS FOR M-POINT BOUNDARY-VALUE PROBLEM WITH ONE-DIMENSIONAL P-LAPLACIAN

摘要

In this paper; we consider the multipoint boundary value problemfor the one-dimensional p-Laplacian ( Φ _ p ( u ' ( t ) ) ) + q(t)f (t, u(t), u'(t) = 0, t ∈ (0, 1), subject to the boundary value.conditions: u(0)=sun from i=1 to (m-2) of a_iu(ξ_i), u(1)=sun from i=1 to (m-2) of b_iu(ξ_i), 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, b_i ∈ [0, 1), 0 ≤ sun from i=1 to (m-2) of a_i<1,0≤sun from i=1 to (m-2) of b_i< 1. Using a fixed pointtheorem 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 the nonlinear term f is involved with the first-order derivative explicitly.