Geodesic
Multiple positive solutions for nonlinear third-order three-point boundary-value problems
Electronic Journal of Differential Equations, Tome 2007 (2007).

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

Summary: This paper concerns the nonlinear third-order three-point boundary-value problem $$\displaylines{ u'''(t)+h(t)f(u(t))=0, \quad t\in (0,1), \cr u(0)=u'(0)=0, \quad u'(1)=\alpha u'(\eta ), }$$ where $0\eta 1$ and $1\alpha \frac 1\eta $. First, we establish the existence of at least three positive solutions by using the well-known Leggett-Williams fixed point theorem. And then, we prove the existence of at least $2m-1$ positive solutions for arbitrary positive integer $m$.
Classification : 34B10, 34B18
Keywords: third-order boundary value problem, positive solution, three-point boundary value problem, existence, cone, fixed point 
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     author = {Guo, Li-Jun and Sun, Jian-Ping and Zhao, Ya-Hong},
     title = {Multiple positive solutions for nonlinear third-order three-point boundary-value problems},
     journal = {Electronic Journal of Differential Equations},
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     volume = {2007},
     year = {2007},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2007__2007__a261/}
}
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Guo, Li-Jun; Sun, Jian-Ping; Zhao, Ya-Hong. Multiple positive solutions for nonlinear third-order three-point boundary-value problems. Electronic Journal of Differential Equations, Tome 2007 (2007). http://geodesic.mathdoc.fr/item/EJDE_2007__2007__a261/