具p-Laplacian非线性奇异边值系统正解的存在性

研究了下面带有p-Laplacian算子的非线性奇异边值系统:(ф_p(u'_i))'+a_i(t)f_i(u₁,u₂)=0, 0＜t＜1,α_iф_p(u_i(0))-β_iф_p(u'_i(0))=0, γ_iф_p(u_i(1))+δ_iф_p(u'_i(1))=0,(i=1,2)正解的存在性。其中ф_p(s)为p-Laplacian 算子，即ф_p(s)=|s|^p-2s, p>1, (ф_p)^-1=ф_q,1/p+1/q=1, α_i＞0, β_i≥0, γ_i＞0, δ_i≥0, i=1,2.这里f_{i是下半连续函数(i=1,2). 通过使用锥上的不动点定理,在相当弱的条件下, 获得了这类奇异边值系统正解的存在性.}

Existence of positive solutions for a nonlinear singular boundary value system with p-Laplacian

The existence of positive solutions for a class of nonlinear singular boundary value systems with p-Laplacian is studied:(ф_p(u'_i))'+a_i(t)f_i(u₁,u₂)=0, 0＜t＜1,α_iф_p(u_i(0))-β_iф_p(u'_i(0))=0, γ_iф_p(u_i(1))+δ_iф_p(u'_i(1))=0,(i=1,2) where ф_p(s)=|s|^p-2s, p>1, (ф_p)^-1=ф_q,1/p+1/q=1, α_i＞0, β_i≥0, γ_i＞0, δ_i≥0, i=1,2. f_{i are lower semi-continuous functions(i=1,2). By using the fixed-point theoremof cone expansion and compression of norm type, the existence of　positive solutions for nonlinear singular boundary value system with　p-Laplacian are obtained.}