一类非齐次p-Kirchhoff型椭圆方程组多解的存在性  

Multiplicity of Solutions for a Class of Non-Homogeneous P-Kirchhoff Elliptic Equations

作　　者：汤楠 陈林 王倩 TANG Nan;CHEN Lin;WANG Qian(College of Mathematics and Statistic,Yili Normal University,YiNing 835000,China)

机构地区：[1]伊犁师范大学数学与统计学院,新疆伊宁835000

出　　处：《数学的实践与认识》2022年第4期206-214,共9页Mathematics in Practice and Theory

基　　金：伊犁师范大学博士科研启动基金项目(2017YSBS08);新疆高校科研计划重点资助项目(XJEDU2016I043)。

摘　　要：研究一类非齐次p-Kirchhoff型椭圆方程组{-M(∫_(RN)|x|^(-ap)|■u|^(p)dx)div(|x|^(-ap)|■u|^(p-2)■u)=α/α+βH(x)|u|^(α-2)u|v|^(β)+λh1(x)|u|^(q-2)u+l1(x),-M(∫_(R^(N))|x|^(-ap)|■v|^(p)dx)div(|x|^(-ap)|■v|^(p-2)■v)=β/α+βH(x)|v|^(β-2)v|u|^(α)+μh2(x)|v|^(q-2)v+l2(x),u(x)→0,v(x)→0,|x|→∞,x∈R^(N),其中λ,μ>0,1<p<N,1<q<p<p(k+1)<α+β<p^(*)=N_(p)/N-pd,0≤a<N-p/p,a≤b<a+1,d=a+1-b>0,M(s)=a+bs^(k),k≥0,H(x),h_(1)(x),h_(2)(x),l_(1)(x)和l_(2)(x)是连续函数且在R^(N)中可变号,运用山路定理和埃克兰变分原理证明了此问题至少存在两个正解.In this paper,we study the existence of multiple solutions for a class of nonhomogeneous p-Kirchhoff elliptic equations{-M(∫_(RN)|x|^(-ap)|■u|^(p)dx)div(|x|^(-ap)|■u|^(p-2)■u)=α/α+βH(x)|u|^(α-2)u|v|^(β)+λh1(x)|u|^(q-2)u+l1(x),-M(∫_(R^(N))|x|^(-ap)|■v|^(p)dx)div(|x|^(-ap)|■v|^(p-2)■v)=β/α+βH(x)|v|^(β-2)v|u|^(α)+μh2(x)|v|^(q-2)v+l2(x),u(x)→0,v(x)→0,|x|→∞,x∈R^(N),whereλ,μ>0,1<p<N,1<q<p<p(k+1)<α+β<p^(*)=N_(p)/N-pd,0≤a<N-p/p,a≤b<a+1,d=a+1-b>0,M(s)=a+bs^(k),k≥0,H(x),h_(1)(x),h_(2)(x),l_(1)(x)and l_(2)(x)are continuous functions that change sign in R^(N).Using the Mountain pass Theorem and Ekeland’s variational principle to prove that problem has at least two positive solutions.

关 键 词：P-Kirchhoff型椭圆方程组 山路定理 埃克兰变分原理 

分 类 号：O175.25[理学—数学]