Multiple positive solutions for a class of (2, p)-Laplacian equation

In this work, we investigate the (2, p)-Laplacian equation -Delta u - Delta(p)u = f (x, u) in Omega with the boundary condition u = 0 on partial derivative Omega, where Omega is a smooth bounded domain in R-N, p > 2, and the nonlinearity f has extension property at both the zero and infinity points. We observe that the above equation admits at least two positive solutions, owing to the mountain pass theorem and Ekeland's variational principle. Published by AIP Publishing.