@article{Lu2024, 
author = {Dengfeng Lu and Shuwei Dai},
title = {On existence results for a class of biharmonic elliptic problems without (AR) condition},
year = {2024},
journal = {AIMS Mathematics},
volume = {9},
number = {7},
pages = {18897-18909},
keywords = {biharmonic elliptic equation, (AR) condition, critical point theory, Nehari manifold, infinitely many solutions, geometrically distinct solutions},
url = {https://www.sciopen.com/article/10.3934/math.2024919},
doi = {10.3934/math.2024919},
abstract = {In this paper, we study the following biharmonic elliptic equation in              R              N      :         Δ          2        ψ  −  Δ  ψ  +  P  (  x  )  ψ  =  g  (  x  ,  ψ  )  ,      x  ∈            R              N        ,where    g and    P are periodic in        x          1        ,  ⋯  ,      x          N      ,    g  (  x  ,  ψ  ) is subcritical and odd in    ψ. Without assuming the Ambrosetti-Rabinowitz condition, we prove the existence of infinitely many geometrically distinct solutions for this equation, and the existence of ground state solutions is established as well.}
}