Existence and concentration of sign-changing solutions to Kirchhoff-type system with Hartree-type nonlinearity

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• 作者：Fuyi Li ; Chunjuan Gao ; Xiaoli Zhu ; ^{zhuxiaoli@sxu.edu.cn}
• 关键词：Kirchhoff-type system ; Hartree-type nonlinearity ; Sign-changing solution ; Concentration
• 刊名：Journal of Mathematical Analysis and Applications
• 出版年：2017
• 出版时间：1 April 2017
• 年：2017
• 卷：448
• 期：1
• 页码：60-80
• 全文大小：458 K
• 卷排序：448

文摘

In this paper, we discuss the existence and the concentration of sign-changing solutions to a class of Kirchhoff-type systems with Hartree-type nonlinearity in R3R3. By the minimization argument on the sign-changing Nehari manifold and a quantitative deformation lemma, we prove that the system has a sign-changing solution. Moreover, concentration behaviors of sign-changing solutions are obtained when the coefficient of the potential function tends to infinity. Specially, our results cover general Schrödinger equations, Kirchhoff equations and Schrödinger–Poisson systems.