@article{Li2022, 
author = {Xia Li and Wen Guan and Da-Bin Wang},
title = {Least energy sign-changing solutions of Kirchhoff equation on bounded domains},
year = {2022},
journal = {AIMS Mathematics},
volume = {7},
number = {5},
pages = {8879-8890},
keywords = {Kirchhoff equation, nonlocal term, variation methods, sign-changing solutions},
url = {https://www.sciopen.com/article/10.3934/math.2022495},
doi = {10.3934/math.2022495},
abstract = {We deal with sign-changing solutions for the Kirchhoff equation         {                            −          (          a          +          b                      ∫                          Ω                                            |                    ∇          u                                    |                                      2                                d          x          )          Δ          u          =          λ          u          +          μ                      |                    u                                    |                                      2                                u          ,                              x          ∈          Ω          ,                                      u          =          0          ,                              x          ∈          ∂          Ω          ,                        where    a  ,  b  >  0 and    λ  ,  μ  ∈      R   being parameters,    Ω  ⊂            R              3       is a bounded domain with smooth boundary    ∂  Ω. Combining Nehari manifold method with the quantitative deformation lemma, we prove that there exists        μ          ∗        >  0 such that above problem has at least a least energy sign-changing (or nodal) solution if    λ  <  a      λ          1       and    μ  >      μ          ∗      , where        λ          1        >  0 is the first eigenvalue of    (  −  Δ  u  ,      H          0              1        (  Ω  )  ). It is noticed that the nonlinearity    λ  u  +  μ      |    u            |              2        u fails to satisfy super-linear near zero and super-three-linear near infinity, respectively.}
}