Geodesic
A note on the singular Sturm-Liouville problem with infinitely many solutions
Electronic Journal of Differential Equations, Tome 2002 (2002).

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: 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 
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     author = {Kosmatov, Nickolai},
     title = {A note on the singular {Sturm-Liouville} problem with infinitely many solutions},
     journal = {Electronic Journal of Differential Equations},
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     volume = {2002},
     year = {2002},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2002__2002__a126/}
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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__a126/