Bulletin of the
Korean Mathematical Society
BKMS

ISSN(Print) 1015-8634 ISSN(Online) 2234-3016

Article

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Bull. Korean Math. Soc. 2012; 49(4): 815-827

Printed July 1, 2012

https://doi.org/10.4134/BKMS.2012.49.4.815

Copyright © The Korean Mathematical Society.

Existence of $n$ positive solutions to second-order multi-point boundary value problem at resonance

Feng Wang and Fang Zhang

Hohai University, Changzhou University

Abstract

The existence of $n$ positive solutions is established for second-order multi-point boundary value problem at resonance where $n$ is an arbitrary natural number. The proof is based on a theory of fixed point index for A-proper semilinear operators defined on cones due to Cremins.

Keywords: boundary value problem, positive solution, resonance, A-proper, fixed point index

MSC numbers: 34B10, 34B15