Geodesic
Multiple positive solutions for nonlinear second-order m-point boundary-value problems with sign changing nonlinearities
Electronic journal of differential equations, Tome 2008 (2008)
In this paper, we study the nonlinear second-order m-point boundary value problem

$\displaylines{ u''(t)+f(t,u)=0,\quad 0\leq t \leq 1, \cr \beta u(0)-\gamma u'(0)=0,\quad u(1)=\sum _{i=1}^{m-2}\alpha_{i} u(\xi_{i}), }$

where the nonlinear term $f$ is allowed to change sign. We impose growth conditions on $f$ which yield the existence of at least two positive solutions by using a fixed-point theorem in double cones. Moreover, the associated Green's function for the above problem is given.
Classification : 34B15
Keywords: m-point, boundary-value problem, Green's function, fixed point theorem in double cones 
@article{EJDE_2008__2008__a61,
     author = {Xu,  Fuyi and Chen,  Zhenbo and Xu,  Feng},
     title = {Multiple positive solutions for nonlinear second-order m-point boundary-value problems with sign changing nonlinearities},
     journal = {Electronic journal of differential equations},
     year = {2008},
     volume = {2008},
     zbl = {1171.34015},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2008__2008__a61/}
}
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%J Electronic journal of differential equations
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%F EJDE_2008__2008__a61
Xu,  Fuyi; Chen,  Zhenbo; Xu,  Feng. Multiple positive solutions for nonlinear second-order m-point boundary-value problems with sign changing nonlinearities. Electronic journal of differential equations, Tome 2008 (2008). http://geodesic.mathdoc.fr/item/EJDE_2008__2008__a61/