Non-even positive solutions of the one-dimensional -Laplace Emden–Fowler equation

We study the one-dimensional p -Laplace Emden–Fowler equation under the Dirichlet boundary condition, where the coefficient function is even in ( − 1 , 1 ) , small for | t | < a , and large for a < | t | < 1 with a close to 1. Then we prove that a least energy solution is not even.