【摘要】 利用Schauder不动点定理研究高阶奇异(k,n-k)共轭边值问题:{(-1)n-kx(n)=f(t,x)+e(t),t∈(0,1),x(i)(0)=0,0≤i≤k-1,x(j)(1)=0,0≤j≤n-k-1,其中f的第一个或第二个变量可以具有奇性,e可以是负的,并给出了几个新的存在性结果.更多还原

【Abstract】 New results on the existence of positive solutions for singular higher differential equations with(k,n-k) conjugate boundary value problem{(-1) n-kx(n) = f(t,x) + e(t),t ∈(0,1),x(i)(0) = 0,0 ≤ i ≤ k-1,x(j)(1) = 0,0 ≤ j ≤ n-k-1,have been obtained,where f may be singular in its first or second variable,e does not need to be positive.The proof relies on Schauder’s fixed point theorem.更多还原