Electronic Journal of Differential Equations,
Vol. 2012 (2012), No. 126, pp. 1-8.

Title: Existence of  positive solutions to three-point $\phi$-Laplacian
       BVPs via homotopic deformations
  
Authors: Nadir Benkaci (Univ. M'Hmed Bouguerra, Boumerdes, Algeria)
         Abdelhamid Benmezai (USTHB, El-Alia Bab-ezouar, Algiers, Algeria)
	 Johnny Henderson (Baylor Univ., Waco, Texas, USA)

Abstract:
 Under suitable conditions and via homotopic deformation, we provide
 existence results for a positive solution to the three-point
 $\phi$-Laplacian   boundary-value problem
 $$\displaylines{
 -( a\phi(u'))'(x)=b(x) f(x,u(x)),\quad  x\in ( 0,1), \cr
 u(0)=\alpha u(\eta),\quad  u'(1)=0,
 }$$
 where $\phi:\mathbb{R}\to\mathbb{R}$ is an increasing homeomorphism
 with $\phi(0) =0$, $b$ does not vanish identically, 
 and $f$ is continuous.

Submitted March 12, 2012. Published August 14, 2012.
Math Subject Classifications: 34B15, 34B18.
Key Words: phi-Laplacian BVP; positive solution; fixed point; index theory.