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Singular boundary value problems for quasi-differential equations. (English) Zbl 0886.34016

This paper presents some existence results for singular quasi-differential equations of the form \[ L_ny+ f(x,L_0y,\dots, L_{n-2}y)=0, \quad L_iy(0)=0,\;0\leq i\leq n-2, \quad L_{n-1} y(1)=0; \] here \(L_i\) denotes the \(i\)th quasiderivative. The nonlinearity \(f\) may be singular at \(y_i=0\), \(1\leq i\leq n-1\). The technique used involves a fixed point theorem for operators that are decreasing with respect to a cone.

MSC:

34B15 Nonlinear boundary value problems for ordinary differential equations
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