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

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 RNRN with N≥4N≥4 and the case that 1