本文選題：漸近線性方程組 + 非平凡解�。� 參考：《中南民族大學(xué)》2015年碩士論文

【摘要】：本文主要考慮三類無窮遠處具有漸近線性的半線性橢圓型方程及方程組的非平凡解的存在性.第一章我們簡單介紹了相關(guān)背景與預(yù)備知識.第二章,我們研究帶有Hardy項的半線性奇異橢圓方程:利用山路定理,證明了當(dāng)f(u)是漸近線性時,方程(0-1)在R~N中非平凡解的存在性.第三章,研究如下帶參數(shù)的半線性橢圓型方程組:其中Ω為R~N中的有界光滑區(qū)域,λ,u非負,N≥3.我們考慮非線性項不滿足增長性條件,證明了如果λμ≥1,方程組(0-2)在H_0~1(Ω)×H_0~1(Ω)中至少有一個非平凡解.第四章,我們研究半線性橢圓型方程組:非平凡解的存在性.其中λμ1且lλ+1,mμ+1由Sobolev嵌入定理可知H_1~1(R~N)緊嵌入到L~P(R~N)中,我們在H_r~1(R~N)中運用變分技巧來討論該問題非平凡解的存在性.
[Abstract]:In this paper, we consider the existence of nontrivial solutions for three kinds of semilinear elliptic equations with asymptote linearity at infinity. In the first chapter, we briefly introduce the relevant background and preparatory knowledge. In chapter 2, we study the semilinear singular elliptic equation with Hardy term: by using the mountain pass theorem, we prove the existence of the nontrivial solution of the equation (0-1) in RGN when f (u) is asymptotically linear. In chapter 3, the following semilinear elliptic equations with parameters are studied: where 惟 is a bounded smooth region in RN, and 位 u is nonnegative n 鈮，

本文編號：2065409