Geodesic
Existence of positive solutions to three-point $\phi$-Laplacian BVPs via homotopic deformations
Electronic Journal of Differential Equations, Tome 2012 (2012).

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

Summary: Under suitable conditions and via homotopic deformation, we provide existence results for a positive solution to the three-point $$\displaylines{ -( a\phi(u'))'(x)=b(x) f(x,u(x)),\quad x\in ( 0,1), \cr u(0)=\alpha u(\eta),\quad u'(1)=0, }$$ where $\phi:\mathbb{R}\to\mathbb{R}$ is an increasing homeomorphism with $\phi(0) =0$, b does not vanish identically, and f is continuous.
Classification : 34B15, 34B18
Keywords: phi-Laplacian BVP, positive solution, fixed point, index theory 
@article{EJDE_2012__2012__a66,
     author = {Benkaci, Nadir and Benmezai, Abdelhamid and Henderson, Johnny},
     title = {Existence of positive solutions to three-point $\phi${-Laplacian} {BVPs} via homotopic deformations},
     journal = {Electronic Journal of Differential Equations},
     publisher = {mathdoc},
     volume = {2012},
     year = {2012},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2012__2012__a66/}
}
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Benkaci, Nadir; Benmezai, Abdelhamid; Henderson, Johnny. Existence of positive solutions to three-point $\phi$-Laplacian BVPs via homotopic deformations. Electronic Journal of Differential Equations, Tome 2012 (2012). http://geodesic.mathdoc.fr/item/EJDE_2012__2012__a66/