本文選題：Kirchhoff型方程　切入點：Neumann邊界　出處：《貴州民族大學(xué)》2017年碩士論文　論文類型：學(xué)位論文

【摘要】：本文利用對稱山路引理、Nehari流形和集中緊性原理,研究了兩類Neumann邊界條件下Kirchhoff型方程的多解性。首先研究如下的Kirchhoff型方程:其中為R3中有光滑邊界的有界開區(qū)域,φ為外法向單位向量.a,b0是兩個實參數(shù),/:Q × R1→R1是Caratheodory函數(shù),滿足次臨界增長條件.當(dāng)函數(shù)f(·)和函數(shù)c(·)滿足某些條件時,我們利用對稱山路引理,得到方程有無窮多非平凡解存在·然后,研究如下帶臨界指數(shù)增長項的Kirchhoff型方程:其中Ω為R3中有光滑邊界的有界開區(qū)域,1q2,ε是充分小的正參數(shù),υ為外法向單位向量·位勢函數(shù)fA定義為:fλ = λf++f-,λ是正實數(shù),f士 = 土 max{±f,0}≠0且f ∈ L6/6-q(Ω).我們利用Nehari流形和集中緊性原理及一些分析技巧,得到方程在臨界條件下至少存在兩個正解,其中一個是正的基態(tài)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 {鹵f 0} 鈮，

本文編號：1609398