@article{Yang2025, 
author = {Yan-Fei Yang and Chun-Lei Tang},
title = {Positive and sign-changing solutions for Kirchhoff equations with indefinite potential},
year = {2025},
journal = {Communications in Analysis and Mechanics},
volume = {17},
number = {1},
pages = {159-187},
keywords = {variational methods, sign-changing solutions, positive solutions, Kirchhoff problem, indefinite potential},
url = {https://www.sciopen.com/article/10.3934/cam.2025008},
doi = {10.3934/cam.2025008},
abstract = {We deal with the nonlinear Kirchhoff problem           −      (          a      +      b                                    ∫                                                              R                                            3                                                              |                ∇        u                              |                    2                          d                x              )    Δ  u  +  V  (  x  )  u  =  f  (  u  )  ,          x  ∈            R              3        ,                                    (          P        )  where    a is a positive constant,    b  >  0 is a parameter, the potential function    V is allowed to change its sign, and the nonlinearity    f  ∈  C  (      R    ,      R    ) exhibits subcritical growth. Under some suitable conditions on    V, we first prove that the problem has a positive ground state solution for all    b  >  0. Then, by using a more general global compactness lemma and a sign-changing Nehari manifold, combined with the method of constructing a sign-changing    (      P    S        )    c   sequence, we show the existence of a least energy sign-changing solution for    b  >  0 that is sufficiently small. Moreover, the asymptotic behavior    b  ↘  0 is established.}
}