Existence of ground state sign‐changing solutions for p ‐Laplacian equations of Kirchhoff type

In this paper, we prove the existence of ground state sign‐changing solutions for the following class of elliptic equation:−1 + b ∫R N| ∇ u | p d x△ p u + V ( x ) | u | p − 2 u = K ( x ) f ( u ) , x ∈ R N ,where u ∈ D 1 , p ( R N ) , p ⩾ 2 , N > p , b > 0 , V ( x ) , and K ( x ) are positive continuous functions. Firstly, we obtain one ground state sign‐changing solution u b by using some new analytical skills and non‐Nehari manifold method. Furthermore, the energy of u b is strictly larger than twice that of the ground state solutions of Nehari type. We also establish the convergence property of u b as the parameter b ↘0. Copyright © 2017 John Wiley & Sons, Ltd.