两类带有临界指数的Kirchhoff型方程的解的存在性和多重性

发布时间：2018-04-26 02:42

  本文选题：Kirchhoff型方程 + 临界指数　； 参考：《西南大学》2015年硕士论文

【摘要】：本文首先利用临界点理论中山路引理得到了无界区域中带有临界指数增长项的Kirchhof型方程的正解的存在性和多重性,然后研究了Dirichlet边界条件下带有临界指数增长项的Kirchhoff型方程的正的基态解的存在性.首先,考虑如下带有临界指数增长项的Kirchhoff型方程我们的主要结果如下.定理1假设并且h满足(h0).那么存在λ*0使得对于所有的λ∈(0,λ*),方程(1)至少有两个不同的正解.其次,考虑如下Dirichlet边界条件下带有临界指数增长项的Kirchhoff型方程其中Ω (?)R3是有界光滑区域,a,b0,并且f满足下列条件：我们有以下结论.定理2假设a,b0,并且f满足(f1)-(f4),那么方程(2)至少存在一个正的基态解.
[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，

本文编号：1804146