Geodesic
Existence of positive solutions to three-point \(\phi\)-Laplacian BVPs via homotopic deformations
Electronic journal of differential equations, Tome 2012 (2012)
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},
     year = {2012},
     volume = {2012},
     zbl = {1260.34040},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2012__2012__a66/}
}
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%J Electronic journal of differential equations
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%F EJDE_2012__2012__a66
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/