Electronic Journal of Differential Equations
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 = infinity. Under an additional condition on the nonlinearity, it is shown that the positive solution is unique for any lambda > 0; thus the continuum 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.
Kim, C. G., & Shi, J. (2012). Global continuum and multiple positive solutions to a p-Laplacian boundary-value problem. Electronic Journal of Differential Equations, 2012(106), 1-12.