Existence of infinitely many solutions of a beam equation with non-monotone nonlinearity

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• 作者：Shaowei Chen ; ^{swchen6@163.com" class="auth_mail" title="E-mail the corresponding author} ; Hai Xu
• 关键词：Critical point theory ; Nonlinear beam equation ; Infinitely many solutions
• 刊名：Nonlinear Analysis: Real World Applications
• 出版年：2017
• 出版时间：February 2017
• 年：2017
• 卷：33
• 期：Complete
• 页码：181-199
• 全文大小：669 K

文摘

In this paper, we prove a new critical point theorem without the ${\left(\mathrm{PS}\right)}^{\ast }$ condition or the ${\left(\mathrm{WPS}\right)}^{\ast }$ condition. Using this theorem, we prove the existence of infinitely many solutions of the following sublinear beam equation Unlike the previous results on this equation, we do not impose any monotone conditions on the variable ξ$\xi$ in the nonlinearity b55c6cae3e52458" title="Click to view the MathML source">f(x,t,ξ)$f(x,t,\xi )$.