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Global Continuum and Multiple Positive Solutions to a P-Laplacian Boundary-Value Problem
Kim, Chan-Gyun Shi, Junping Shi, Junping
Kim, Chan-Gyun
Shi, Junping
Shi, Junping
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 > 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.
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2012-01-01
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Mathematics