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Singular nonlinear multipoint conjugate boundary value problems. (English) Zbl 0903.34016

The authors prove the existence of solutions for the multipoint conjugate boundary value problem

y (n) =f(x,y),x[0,1]{a 1 ,a 2 ,,a k },(1)
y (j) (a i )=0,0jn i -1,1ik,(2)

where 0=a 1 <a 2 <<a k =1 are fixed and f(x,y) has a singularity at y=0. The approach of the authors is to construct a sequence of perturbations of f which terms lack the singularity of f and to apply a fixed point theorem to the respective boundary value problems. It is shown that the obtained sequence of iterates converges to a solution to (1), (2).

MSC:
34B10Nonlocal and multipoint boundary value problems for ODE
34B15Nonlinear boundary value problems for ODE