Electronic Journal of Differential Equations,
Vol. 2012 (2012), No. 106, pp. 1-12.

Title: Global continuum and multiple positive solutions to
       a p-Laplacian boundary-value problem.

Authors: Chan-Gyun Kim (College of William and Mary, Williamsburg, VA, USA)
         Junping Shi   (College of William and Mary, Williamsburg, VA, USA)

Abstract:
 A p-Laplacian boundary-value problem with positive nonlinearity
 is considered. The existence of a continuum  of positive solutions
 emanating from $(\lambda,u)=(0,0)$ is shown, and it can be extended
 to $\lambda=\infty$. Under an additional condition on the nonlinearity,
 it is shown that the positive solution is unique for any $\lambda>0$;
 thus the continuum $\mathcal{C}$ is indeed a continuous curve globally
 defined for all $\lambda>0$. In addition, by the upper and lower solutions
 method,  existence of three positive solutions is established under some
 conditions on the nonlinearity.

Submitted May 25, 2012. Published June 25, 2012.
Math Subject Classifications: 34B18, 34C23, 35J25.
Key Words: Upper and lower solution; positive solution;
           p-Laplacian; uniqueness; multiplicity.