Soliton solutions for quasilinear Schrödinger equations with critical growth
Soliton solutions for quasilinear Schrödinger equations with critical growth
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DOI：
10.1016/j.jde.2009.11.030
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发表时间：
2010-02
影响因子：
2.4
通讯作者：
João Marcos;O. Miyagaki;S. Soares
中科院分区：
文献类型：
--
作者：
João Marcos;O. Miyagaki;S. Soares
本文建立了一类含临界增长的拟线性薛定谔方程驻波解的存在性。通过变量变换，将拟线性方程组化为半线性方程组，其相应的泛函在通常的Sobolev空间中定义良好，并满足山路定理的几何条件.利用这一事实，我们得到了一个弱收敛于解v的Cerami序列。在证明v是非平凡的过程中，主要工具是P.L. Lions的一些经典论点，并结合H. Brezis和L. Nirenberg（1983）in [9].
In this paper we establish the existence of standing wave solutions for quasilinear Schrödinger equations involving critical growth. By using a change of variables, the quasilinear equations are reduced to semilinear one, whose associated functionals are well defined in the usual Sobolev space and satisfy the geometric conditions of the mountain pass theorem. Using this fact, we obtain a Cerami sequence converging weakly to a solution v. In the proof that v is nontrivial, the main tool is the concentration–compactness principle due to P.L. Lions together with some classical arguments used by H. Brezis and L. Nirenberg (1983) in [9].