Positive solutions for a quasilinear Schrödinger equation involving Hardy potential and critical exponent
Positive solutions for a quasilinear Schrödinger equation involving Hardy potential and critical exponent
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DOI：
10.1142/s0219199714500345
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发表时间：
2014-11
影响因子：
1.6
通讯作者：
Xiaoyu Zeng;Yimin Zhang;Huan-Song Zhou
中科院分区：
文献类型：
--
作者：
Xiaoyu Zeng;Yimin Zhang;Huan-Song Zhou
我们关注具有 Hardy 势和临界指数的拟线性薛定谔方程的正解。与半线性方程不同，我们方程中的Hardy项不仅是奇异的，而且是非线性的。通过使用 Nehari 方法作为 Liu-Liu-Wang [具有临界增长的拟线性薛定谔方程的基态，计算，似乎不太可能在 H-1(R-N) 布尔 AND L-无穷大(R-N) 中获得方程的解。变种。偏微分方程46（2013）641-669]。本文通过将拟线性方程转化为半线性方程，在适当的条件下建立了H-1(R-N)中拟线性薛定谔方程正解的存在性。
We are concerned with positive solutions of a quasilinear Schrodinger equation with Hardy potential and critical exponent. Different from the semilinear equation, the Hardy term in our equation is not only singular, but also nonlinear. It seems unlikely to get solutions for our equation in H-1(R-N) boolean AND L-infinity(R-N) by using Nehari method as Liu-Liu-Wang [Ground states for quasilinear Schrodinger equations with critical growth, Calc. Var. Partial Differential Equations 46 (2013) 641-669]. In this paper, by transforming the quasilinear equation to a semilinear equation, we established the existence of positive solutions for the quasilinear Schrodinger equation in H-1(R-N) under suitable conditions.