黎曼流形上一类奇摄动耦合椭圆型方程组的标量曲率的作用
The role of the scalar curvature in some singularly perturbed coupled elliptic systems on Riemannian manifolds
摘要：
给定一个三维黎曼流形（M，g），研究了M上具有次临界非线性项的奇摄动Klein-Gordon-Maxwell系统和Schroedinger-Maxwell系统正解的存在性.我们证明了当扰动参数λ足够小时，流形（M，g）的标量曲率的任何稳定临界点x_0产生两个系统的正解（u_eps，v_eps），使得当λ趋于零时，u_eps集中在xi_0.
英文摘要：
Given a 3-dimensional Riemannian manifold (M,g), we investigate the existence of positive solutions of singularly perturbed Klein-Gordon-Maxwell systems and Schroedinger-Maxwell systems on M, with a subcritical nonlinearity. We prove that when the perturbation parameter epsilon is small enough, any stable critical point x_0 of the scalar curvature of the manifold (M,g) generates a positive solution (u_eps,v_eps) to both the systems such that u_eps concentrates at xi_0 as epsilon goes to zero.
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