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Bounded solutions for singular boundary value problems. (English) Zbl 0642.34030
Let T be the set obtained by removing k points (counting multiplicities) from [0,1]. Let $$A_ i$$ be an invertible matrix-valued function in T with real entries of class $$C^ i(T)$$, $$i=1,...,k$$, and let $$B_ j$$ be a real continuous matrix-valued function in T for $$j=0,...,p$$. Boundary value problems are considered for the vector-matrix differential equation $DA_ 1(t)... DA_ k(t)D^ px+\sum^{p}_{j=0}B_ j(t)D^ jx=f(t,x,...,x^{(p+q-1)})$ in T, with homogeneous boundary conditions at p points in [0,1], where $$1\leq q\leq k$$, $$D=d/dt$$. Conditions are given for which such singular boundary value problems have solutions $$x\in C^{p+k}(T,R^ n)$$ extendible to $$C^{p-1}([0,1],R^ n).$$
##### MSC:
 34C11 Growth and boundedness of solutions to ordinary differential equations 34B10 Nonlocal and multipoint boundary value problems for ordinary differential equations 34B15 Nonlinear boundary value problems for ordinary differential equations
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##### References:
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