The existence of countably many positive solutions for a system of nonlinear singular boundary value problems with the p-Laplacian operator

In this paper, we study the existence of countable many positive solutions for a class of nonlinear singular boundary value systems with p-Laplacian operator: (φp1(u )) +a1(t)f (u, v) = 0, 0 < t <1, (φp2 (v )) +a2(t)g(u, v) = 0, 0 < t <1, α1φp1 (u(0)) −β1φp1(u (0)) = 0, γ1φp1 (u(1)) +δ1φp1(u (1)) = 0, α2φp2 (v(0))−β2φp2 (v (0)) = 0, γ2φp2 (v(1))+δ2φp2 (v (1)) = 0, where φpi (s) = |s|pi−2s, pi > 1, f , g are lower semi-continuous functions, ai (t) has countable many singularities on (0, 1/2), i = 1, 2. By using the fixed-point theorem of cone expansion and compression of norm type, the existence of countable many positive solutions for nonlinear singular boundary value system with p-Laplacian operator are obtained. © 2006 Elsevier Inc. All rights reserved.