Geodesic
A note on the singular Sturm-Liouville problem with infinitely many solutions
Electronic journal of differential equations, Tome 2002 (2002)
We consider the Sturm-Liouville nonlinear boundary-value problem

$ \displaylines{ -u''(t) = a(t)f(u(t)), \quad 0 less than t less than 1, \cr \alpha u(0) - \beta u'(0) =0, \quad \gamma u(1) + \delta u'(1) = 0, } $

where $\alpha, \beta, \gamma, \delta \geq 0, \alpha \gamma + \alpha \delta + \beta \gamma greater than 0$ and $a(t)$ is in a class of singular functions. Using a fixed point theorem we show that under certain growth conditions imposed on $f(u)$ the problem admits infinitely many solutions.
Classification : 34B16, 34B18
Keywords: Sturm-Liouville problem, Green's function, fixed point theorem, Hölder's inequality, multiple solutions 
@article{EJDE_2002__2002__a26,
     author = {Kosmatov,  Nickolai},
     title = {A note on the singular {Sturm-Liouville} problem with infinitely many solutions},
     journal = {Electronic journal of differential equations},
     year = {2002},
     volume = {2002},
     zbl = {1026.34023},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2002__2002__a26/}
}
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Kosmatov,  Nickolai. A note on the singular Sturm-Liouville problem with infinitely many solutions. Electronic journal of differential equations, Tome 2002 (2002). http://geodesic.mathdoc.fr/item/EJDE_2002__2002__a26/