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Acta Mathematicae Applicatae Sinica
, Volume 18 (2) – Jan 1, 2002

/lp/springer-journals/boundary-value-problems-for-singular-second-order-functional-o5On6eQs6b

- Publisher
- Springer Journals
- Copyright
- Copyright © 2002 by Springer-Verlag Berlin Heidelberg
- Subject
- Mathematics; Applications of Mathematics; Math Applications in Computer Science; Theoretical, Mathematical and Computational Physics
- ISSN
- 0168-9673
- eISSN
- 1618-3932
- DOI
- 10.1007/s102550200023
- Publisher site
- See Article on Publisher Site

Positive solutions to the boundary value problem, $$ \left\{ {\begin{array}{*{20}l} {{{y}\ifmmode{''}\else$''$\fi = - f{\left( {x,y{\left( {w{\left( x \right)}} \right)}} \right)},} \hfill} & {{0 < x < 1,} \hfill} \\ {{\alpha y{\left( x \right)} - \beta {y}\ifmmode{'}\else$'$\fi{\left( x \right)} = \xi {\left( x \right)},} \hfill} & {{a \leqslant x \leqslant 0,} \hfill} \\ {{\gamma y{\left( x \right)} + \delta {y}\ifmmode{'}\else$'$\fi{\left( x \right)} = \eta {\left( x \right)},} \hfill} & {{1 \leqslant x \leqslant b,} \hfill} \\ \end{array} } \right. $$ are obtained by applying the Schauder fixed point theorem, where w(x) is a continuous function defined on [0, 1] and f(x, y) is a function defined on (0, 1)×(0, ∞), which satisfies certain restrictions and may have singularity at y=0. The result corrects and improves an existence theorem due to Erbe and Kong[1].

Acta Mathematicae Applicatae Sinica – Springer Journals

**Published: ** Jan 1, 2002

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