Electron. J. Differential Equations, Vol. 2016 (2016), No. 273, pp. 1-8.

Solvability of singular second-order initial-value problems

Petio Kelevedjiev

This article concerns the solvability of the initial-value problem x''=f(t,x,x'), x(0)=A, x'(0)=B, where the scalar function f may be unbounded as $t\to 0$. Using barrier strip type arguments, we establish the existence of monotone and/or positive solutions in $C^1[0,T]\cap C^2(0,T]$.

Submitted April 8, 2016. Published October 12, 2016.
Math Subject Classifications: 34A12, 34A36.
Key Words: Initial value problem; second order differential equation; singularity; existence; barrier conditions.

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Petio Kelevedjiev
Technical University of Sofia
Branch Sliven, Bulgaria
email: keleved@mailcity.com

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