Neumann边界条件下Kirchhoff型方程的多解性

发布时间：2018-03-14 03:29

  本文选题：Kirchhoff型方程　切入点：Neumann边界　出处：《贵州民族大学》2017年硕士论文　论文类型：学位论文

【摘要】：本文利用对称山路引理、Nehari流形和集中紧性原理,研究了两类Neumann边界条件下Kirchhoff型方程的多解性。首先研究如下的Kirchhoff型方程:其中为R3中有光滑边界的有界开区域,φ为外法向单位向量.a,b0是两个实参数,/:Q × R1→R1是Caratheodory函数,满足次临界增长条件.当函数f(·)和函数c(·)满足某些条件时,我们利用对称山路引理,得到方程有无穷多非平凡解存在·然后,研究如下带临界指数增长项的Kirchhoff型方程:其中Ω为R3中有光滑边界的有界开区域,1q2,ε是充分小的正参数,υ为外法向单位向量·位势函数fA定义为:fλ = λf++f-,λ是正实数,f士 = 土 max{±f,0}≠0且f ∈ L6/6-q(Ω).我们利用Nehari流形和集中紧性原理及一些分析技巧,得到方程在临界条件下至少存在两个正解,其中一个是正的基态解.
[Abstract]:In this paper, by using the symmetric mountain pass Lemma, the Nehari manifold and the principle of centralization compactness are used. In this paper, we study the multiplicity of solutions for Kirchhoff type equations under two kinds of Neumann boundary conditions. Firstly, we study the following Kirchhoff type equations: where 蠁 is a bounded open domain with smooth boundary in R3, 蠁 is an external normal unit vector .aB0 is two real parameters, / / Q 脳 R1. 鈫扺hen the function f (路) and the function c (路) satisfy some conditions, we obtain the existence of infinite nontrivial solutions of the equation by using the symmetric mountain pass Lemma. The following Kirchhoff type equations with critical exponential growth term are studied: where 惟 is a bounded open region with smooth boundary in R3, 蔚 is a sufficiently small positive parameter, and v is an external normal unit vector 路potential function fA is defined as: F 位 = 位 ff -, 位 is a positive real number. Max {卤f 0} 鈮，

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