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.