太原理工大学学报2018，Vol.49Issue(2)：308-312,5.DOI:10.16355/j.cnki.issn1007-9432tyut.2018.02.020
RN上一类非线性Schrödinger-Kirchhoff型方程非平凡解的存在性和多重性
Existence and Multiplicity of Solutions for Nonlinear Schr?dinger-Kirchhoff-Type Equations in RN
摘要
Abstract
The existence and multiplicity of nontrivial solutions for Schr?dinger-Kirchhoff type equations in RNwith subcritical nonlinearities term were investigated by using variational methods.Firstly,it was proved that the energy functional is bounded from below and satisfies (PS)condition under certain assumptions,thus giving a critical value of the energy functional. Then it was proved that the equation has at least a nontrivial solution.Furtherly,it was proved that the equation has infinitely many nontrivial solutions by combining with genus properties when the nonlinear term is odd.关键词
Schrödinger-Kirchhoff型方程/次临界/非平凡解/变分方法/亏格Key words
Schrödinger-Kirchhoff-type equation/subcritical/nontrivial solutions/variational methods/genus分类
数理科学引用本文复制引用
惠艳梅,郭祖记..RN上一类非线性Schrödinger-Kirchhoff型方程非平凡解的存在性和多重性[J].太原理工大学学报,2018,49(2):308-312,5.基金项目
国家自然科学青年基金资助项目(11601363) （11601363）
