Journal of Differential Equations
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.
An, Y., Kim, C. G., & Shi, J. (2016). Exact multiplicity of positive solutions for a p-Laplacian equation with positive convex nonlinearity. Journal of Differential Equations, 260(3), 2091-2118.