本文選題：Kirchhoff型方程 + 臨界指數(shù)�。� 參考：《西南大學》2015年碩士論文

【摘要】：本文首先利用臨界點理論中山路引理得到了無界區(qū)域中帶有臨界指數(shù)增長項的Kirchhof型方程的正解的存在性和多重性,然后研究了Dirichlet邊界條件下帶有臨界指數(shù)增長項的Kirchhoff型方程的正的基態(tài)解的存在性.首先,考慮如下帶有臨界指數(shù)增長項的Kirchhoff型方程我們的主要結(jié)果如下.定理1假設并且h滿足(h0).那么存在λ*0使得對于所有的λ∈(0,λ*),方程(1)至少有兩個不同的正解.其次,考慮如下Dirichlet邊界條件下帶有臨界指數(shù)增長項的Kirchhoff型方程其中Ω (?)R3是有界光滑區(qū)域,a,b0,并且f滿足下列條件：我們有以下結(jié)論.定理2假設a,b0,并且f滿足(f1)-(f4),那么方程(2)至少存在一個正的基態(tài)解.
[Abstract]:In this paper, the existence and multiplicity of positive solutions of Kirchhof type equation with critical exponential growth term in unbounded region are obtained by using the mountain pass Lemma in critical point theory. Then the existence of positive ground state solutions for Kirchhoff type equation with critical exponential growth term under Dirichlet boundary condition is studied. First, we consider the following Kirchhoff type equations with critical exponential growth term. Our main results are as follows. Theorem 1 hypothesizes and h satisfies H0. Then there exists 位 0 such that there are at least two different positive solutions for all 位 鈭，

本文編號：1804146