具有L2-约束的非线性Choquard方程的多解性
Multiple Solutions for Nonlinear Choquard Equation with L2-Constraint

本文考虑如下非线性Choquard方程其中a,b > 0 ，α∈(0,3)，是Riesz位势。g(ξ)∈C(？, ？)满足Berestycki-Lions条件且其为奇或偶的。μ∈？是Lagrange乘子。Wu证明了(1)关于(u,κ)等同于如下系统：在Palais-Smale-Pohozaev条件下，发展新的形变理论，使之在L²-约束问题中能应用极大极小理论并且证明该系统存在无穷多解，因此可证非线性Choquard方程也存在无穷多解。本文处理L²-约束问题，即∫_？³|u|²dx=m。
In this paper, we consider the following nonlinear Choquard equation wherea,b > 0 ，α∈(0,3)，is a Riesz potential. g(ξ)∈C(？, ？) satisfies Berestycki-Lions condition and it is odd or even. μ∈？ is a Lagrange multiplier. Wu proved that (1) is equivalent to the following system with respect to (u,κ): We develop a new deformation argument under Palais-Smale-Pohozaev condition. It enables us to apply minimax argument for L²-constraint problem and we can prove the system exists infinitely many solutions, so we also prove Nonlinear Choquard Equation exists infinitely many solutions. In this paper, we deal with L²-constraint problem, i.e. ∫_？³|u|²dx=m.