一类含凹项的分数阶Kirchhoff方程变号解的存在性和多重性  

Existence and Multiplicity of Sign-changing Solutions for a Class of Fractional Kirchhoff Equations with Concave Term

作　　者：蔡序军 吴克晴[1] CAI Xu-jun;WU Ke-qing(School of Science,Jiangxi University of Science and Technology,Ganzhou 341000,China)

机构地区：[1]江西理工大学理学院,江西赣州341000

出　　处：《长春师范大学学报》2023年第10期12-22,54,共12页Journal of Changchun Normal University

基　　金：国家自然科学基金项目“向量变分不等式投影型方法研究”(61364015)。

摘　　要：研究了一类含凹项的分数阶Kirchhoff方程变号解的存在性和多重性,利用下降流不变集方法验证了变号解的存在性,借助属和相对属得到了变号解的多重性,并且确定了节点域数界.研究结果改进并推广了已知结果.The existence and multiplicity of sign-changing solutions for a class of fractional Kirchhoff equations with concave term are studied.The existence of the sign-changing solution is verified by using the invariant set of descending flow method.The multiplicity of the sign-changing solution is obtained by means of genus and relative genus,and the node domain number bound is determined.The results obtained generalize and improve the known results.

关 键 词：分数阶Kirchhoff方程 变号解 凹项 下降流不变集 属和相对属 

分 类 号：O175.29[理学—数学]