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Singular (k,n-k) boundary value problems between conjugate and right focal. (English) Zbl 0901.34026
Boundary value problems (1) (-1) n-k y (n) =f(x,y), 0<x<1, y (i) (0)=0, 0ik-1, y (i) (1)=0, qjn-k+q-1, whith 1kn-1, 0qk-1, and f(x,y) is singular at y=0, are solved by using a fixed point theorem for decreasing operators in a partially ordered Banach space. The problem (1) is reduced to a lower-order conjugate boundary value problem and this is approximated by a sequence of perturbed boundary value problems which contain no singularity. To each term of that sequence the fixed point theorem is applied and finally a positive solution y(x) to (1) is obtained such that y (i) (x)>0 on (0,1), 0iq.
MSC:
34B15Nonlinear boundary value problems for ODE
47J25Iterative procedures (nonlinear operator equations)
34B27Green functions