Maximal saddle solution of a nonlinear elliptic equation involving the p-Laplacian

Abstract

A saddle solution is called maximal saddle solution if its absolute value is not smaller than those absolute values of any solutions that vanish on the Simons cone C ={ s = t} and have the same sign as s − t. We prove the existence of a maximal saddle solution of the nonlinear elliptic equation involving the p-Laplacian, by using the method of monotone iteration, −� pu = f( u) in R 2m , where 2m ≥ p> 2.