Geodesic
Twin Positive Solutions of Second-Order $m$-Point Boundary Value Problem with Sign Changing Nonlinearities
Bulletin of the Malaysian Mathematical Society, Tome 37 (2014) no. 1 Cet article a éte moissonné depuis la source Bulletin of the Malaysian Mathematical Society website

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In this paper, we study second-order $m$-point boundary value problem

$%\left\{\begin{array}{lll} \begin{cases} u''(t)+a(t)u'(t)+f(t,u)=0, 0 \leq t \leq 1, \\ %\cr\noalign{\vskip 2mm} u'(0)=0, \quad u(1)=\sum _{i=1}^{k}a_iu(\xi_{i})-\sum _{i=k+1}^{m-2}a_{i} u(\xi_{i}), %\end{array}\right. \end{cases}$

where $a_{i}>0(i=1,2,\ldots, m-2), 0\sum _{i=1}^{k}a_i-\sum_{i=k+1}^{m-2}a_{i}1, 0\xi_{1}\xi_{2}\cdots\xi_{m-2}1$, $a\in C([0,1],(-\infty, 0))$ and $f$ is allowed to change sign. We show that there exist two positive solutions by using Leggett-Williams fixed-point theorem. The conclusions in this paper essentially extend and improve some known results.
Classification : 34B15, 34B25 
@article{BMMS_2014_37_1_a24,
     author = {Fuyi Xu and Xiaoyan Guan},
     title = {Twin {Positive} {Solutions} of {Second-Order} $m${-Point} {Boundary} {Value} {Problem} with {Sign} {Changing} {Nonlinearities}},
     journal = {Bulletin of the Malaysian Mathematical Society},
     year = {2014},
     volume = {37},
     number = {1},
     url = {http://geodesic.mathdoc.fr/item/BMMS_2014_37_1_a24/}
}
TY  - JOUR
AU  - Fuyi Xu
AU  - Xiaoyan Guan
TI  - Twin Positive Solutions of Second-Order $m$-Point Boundary Value Problem with Sign Changing Nonlinearities
JO  - Bulletin of the Malaysian Mathematical Society
PY  - 2014
VL  - 37
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/BMMS_2014_37_1_a24/
ID  - BMMS_2014_37_1_a24
ER  - 
%0 Journal Article
%A Fuyi Xu
%A Xiaoyan Guan
%T Twin Positive Solutions of Second-Order $m$-Point Boundary Value Problem with Sign Changing Nonlinearities
%J Bulletin of the Malaysian Mathematical Society
%D 2014
%V 37
%N 1
%U http://geodesic.mathdoc.fr/item/BMMS_2014_37_1_a24/
%F BMMS_2014_37_1_a24
Fuyi Xu; Xiaoyan Guan. Twin Positive Solutions of Second-Order $m$-Point Boundary Value Problem with Sign Changing Nonlinearities. Bulletin of the Malaysian Mathematical Society, Tome 37 (2014) no. 1. http://geodesic.mathdoc.fr/item/BMMS_2014_37_1_a24/