Ground state solutions for Kirchhoff type equations with asymptotically 4-linear nonlinearity

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• 作者：Dongdong Qin^a ; ^{qindd132@163.com" class="auth_mail" title="E-mail the corresponding author} ; Yubo He^a ; ^b ; ^{heyinprc@csu.edu.cn" class="auth_mail" title="E-mail the corresponding author} ; Xianhua Tang^a ; ^{tangxh@mail.csu.edu.cn" class="auth_mail" title="E-mail the corresponding author}
• 关键词：Kirchhoff type equations ; Variational method ; Asymptotically 4-linear ; Nehari manifold ; Ground state
• 刊名：Computers & Mathematics with Applications
• 出版年：2016
• 出版时间：April 2016
• 年：2016
• 卷：71
• 期：7
• 页码：1524-1536
• 全文大小：409 K

文摘

This paper is concerned with the following Kirchhoff type equation: Assuming that the primitive of f$f$ is asymptotically 4-linear as i3" class="mathmlsrc">i3.gif&_user=111111111&_pii=S0898122116300918&_rdoc=1&_issn=08981221&md5=e14ed78543113efa8a290c1d51f72d7a" title="Click to view the MathML source">|v|→∞, a homeomorphism between the Nehari manifold and a subset of unit sphere is constructed based on some observations and new techniques. Inspired by recent work of Szulkin and Weth (2010), ground state solutions for the equation above are obtained, as well as infinitely many pairs of nontrivial solutions for case f(x,v)$f(x,v)$ ​is odd with respect to v$v$.