Document Type
Article
Department/Program
Mathematics
Journal Title
Journal of Differential Equations
Pub Date
2016
Volume
260
Issue
3
First Page
2091
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.
Recommended Citation
An, Yulian; Kim, Chan-Gyun; and Shi, Junping, Exact multiplicity of positive solutions for a p-Laplacian equation with positive convex nonlinearity (2016). Journal of Differential Equations, 260(3), 2091-2118.
10.1016/j.jde.2015.09.058
DOI
10.1016/j.jde.2015.09.058
