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Exact multiplicity of positive solutions for a p-Laplacian equation with positive convex nonlinearity

An, Yulian
; 
Kim, Chan-Gyun
; 
Shi, Junping
Abstract
A p-Laplacian nonlinear elliptic equation with positive and p-superlinear nonlinearity and Dirichlet boundary condition is considered. We first prove the existence of two positive solutions when the spatial domain is symmetric or strictly convex by using a priori estimates and topological degree theory. For the ball domain in R-N with N >= 4 and the case that 1 < p < 2, we prove that the equation has exactly two positive solutions when a parameter is less than a critical value. Bifurcation theory and linearization techniques are used in the proof of the second result. (C) 2015 Elsevier Inc. All rights reserved.
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2016-01-01
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Mathematics
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Mathematics
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10.1016/j.jde.2015.09.058
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https://scholarworks.wm.edu/handle/internal/1823
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