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Existence of solutions of a kind of singular boundary value problem. (English) Zbl 0790.34027
The paper deals with solvability of the singular boundary value problem (BVP) 1 q(t)(p(t)u ' ) ' =f(t,u,pu ' ), t(0,1), u(t) continuous at t=0, u(1)=0, where p,qC[0,1], p,q>0 on (0,1] and p(0)=0, i.e., singularity is at t=0. It is also supposed that 0 1 p -1 (t)dt= since if this integral is convergent, the considered BVP can be transformed into a regular one. The conditions imposed on the nonlinearity f are weaker than similar conditions given by D. R. Dunninger and J. C. Kurtz [J. Math. Anal. Appl. 115, 369-405 (1986; Zbl 0616.34012)]. The principal method used in the proof of the main statement is the method of upper and lower solutions.
Reviewer: O.Došlý (Brno)

34B15Nonlinear boundary value problems for ODE
34E15Asymptotic singular perturbations, general theory (ODE)