Multiple solutions for asymptotically (p −1)-homogeneous p-Laplacian equations

We consider a nonlinear elliptic equation driven by the p-Laplacian and with a reaction term which exhibits a (p − 1)-homogeneous growth both near ±∞ and near zero. Using critical point theory with truncation techniques, the method of upper–lower solutions and Morse theory, we show that the problem has five nontrivial smooth solutions, four of which have constant sign (two positive and two negative). © 2011 Elsevier Inc. All rights reserved.