渐近线性基尔霍夫型方程的解的存在性  

Existence of solutions for asymptotically linear Kirchhoff equations

作　　者：张雪 孙燕 栾世霞[1] ZHANG Xue;SUN Yan;LUAN Shixia(School of Mathematical Sciences,Qufu Normal University,273165,Qufu;Primary School of Gaomi Chongxian,261500,Gaomi,Shandong,PRC)

机构地区：[1]曲阜师范大学数学科学学院,山东曲阜273165 [2]高密市崇贤小学,山东高密261500

出　　处：《曲阜师范大学学报（自然科学版）》2020年第2期19-25,共7页Journal of Qufu Normal University(Natural Science)

摘　　要：研究基尔霍夫型方程a+λ∫R N|▽u|2+V(x)u 2[-Δu+V(x)u]=K(x)f(u),in R N,其中N≥3,a>1,λ≥0是一个参数,并且f(t)在无穷远处是渐近线性的.通过变分的方法,在对K(x)作出适当的假设下可以得到方程的非平凡解的存在性.利用截断函数得到有界的PS序列.In this paper,we study the following Kirchhoff type equation a+λ∫R N|▽u|2+V(x)u 2[-Δu+V(x)u]=K(x)f(u),in R N,where N≥3,a>1,λ≥0 is a parameter,and f(t)is asymptotically linear at infinity.By using variational methods,we obtain the existence of nontrivial solutions under appropriate assumptions on K(x).A cut-off functional is utilized to obtain the bounded Palais-Smale sequences.

关 键 词：基尔霍夫型方程 渐近线性 截断函数 变分方法 

分 类 号：O177.91[理学—数学]