四阶非局部基尔霍夫方程的多重解  

Multiplicity results for nonlocal fourth-order Kirchhoff equations

作　　者：张海燕 莫帅 赵月云 毛安民[1] ZHANG Haiyan;MO Shuai;ZHAO Yueyun;MAO Anmin(School of Mathematical Sciences,Qufu Normal University,273165,Qufu,Shandong,PRC)

机构地区：[1]曲阜师范大学数学科学学院,山东省曲阜市273165

出　　处：《曲阜师范大学学报（自然科学版）》2021年第2期1-6,共6页Journal of Qufu Normal University(Natural Science)

基　　金：国家自然科学基金(11471187).

摘　　要：研究如下四阶基尔霍夫椭圆型方程{Δ^(2)u-(a+b∫_(R3)|▽u|^(2)d x)Δu+V(x)u=q(x)f(x,u),x∈^(3),u∈H 2(ℝ3),其中Δ^(2)=Δ(Δ)为双调和算子,a,b>0为常数,且势函数V(x)∈C(R^(3),R).在合理的假设下,通过使用变分法获得了此方程的基态解和山路解.In this paper,we concern with the following fourth order elliptic equations of Kirchhoff type{Δ^(2)u-(a+b∫_(R3)|▽u|^(2)dx)Δu+V(x)u=q(x)f(x,u),x∈R^(3),u∈H^(2)(R^(3)),whereΔ^(2)=Δ(Δ)is the bi-harmonic operator,a,b>0 are constants,and V(x)∈C(R^(3),R).Under appropriate assumptions,the existence of mountain-pass solution and a ground state solution is obtained by using the variational methods.

关 键 词：基态解 山路解 变分法 

分 类 号：O175.8[理学—数学]