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 = infinity. Under an additional condition on the nonlinearity, it is shown that the positive solution is unique for any lambda \u3e 0; thus the continuum C is indeed a continuous curve globally defined for all lambda \u3e 0. In addition, by the upper and lower solutions method, existence of three positive solutions is established under some conditions on the nonlinearity

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