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

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.

Keywords

• Upper and lower solution
• positive solution
• p-Laplacian
• uniqueness
• multiplicity