Bifurcation from infinity of the Schrodinger equation via invariant manifolds
Bifurcation from infinity of the Schrodinger equation via invariant manifolds
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通过不变流形从薛定谔方程的无穷大分叉
DOI：
10.1016/j.na.2021.112490
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发表时间：
2021
期刊：
影响因子：
--
通讯作者：
Jintao Wang
中科院分区：
文献类型：
--
作者：
Chunqiu Li;Jintao Wang
本文研究了非线性Schrödinger方程的无穷分岔问题。$$−\Delta u+V(x)u=\lambda u + f(x,u),\;\;\;x\in\mathbb{R}^N.$$。我们在动力系统的框架下，考虑无界区域上相应的抛物方程来处理这个问题。首先，我们建立了RN上抛物方程的全局不变流形。然后，我们将抛物方程限制在这个不变流形上，从而生成一个有限维的系统。最后，利用Conley指标理论和吸引子形状理论，在适当的Landesman-Lazer型条件下，建立了Schrödinger方程的无穷分岔和多重解的一些新结果。
This paper is concerned with the bifurcation from infinity of the nonlinear Schrödinger equation.$$−\Delta u+V(x)u=\lambda u + f(x,u),\;\;\;x\in\mathbb{R}^N.$$.We treat this problem in the framework of dynamical systems by considering the corresponding parabolic equation on unbounded domains. Firstly, we establish a global invariant manifold for the parabolic equation on RN. Then, we restrict the parabolic equation to this invariant manifold, which generates a system of finite dimension. Finally, we use the Conley index theory and the shape theory of attractors to establish some new results on bifurcations from infinity and multiplicity of solutions of the Schrödinger equation under an appropriate Landesman–Lazer type condition.