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Existence of ground state sign‐changing solutions for p ‐Laplacian equations of Kirchhoff type
Author(s) -
Chen Jianhua,
Tang Xianhua,
Gao Zu
Publication year - 2017
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.4370
Subject(s) - nehari manifold , mathematics , ground state , sign (mathematics) , type (biology) , p laplacian , manifold (fluid mechanics) , lambda , mathematical analysis , convergence (economics) , pure mathematics , state (computer science) , laplace operator , energy (signal processing) , mathematical physics , nonlinear system , physics , quantum mechanics , mechanical engineering , ecology , algorithm , engineering , economics , biology , boundary value problem , economic growth , statistics
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.