Non-degeneracy and existence of new solutions for the Schrodinger equations

作者：Guo, Yuxia; Musso, Monica; Peng, Shuangjie; Yan, Shusen^*

来源：Journal of Differential Equations, 2022, 326: 254-279.

DOI：10.1016/j.jde.2022.04.016

• PERTURBED ELLIPTIC-EQUATIONS
• SEMICLASSICAL STATES
• MULTIPEAK SOLUTIONS
• POSITIVE SOLUTIONS
• BOUND-STATES
• SYMMETRY
• UNIQUENESS
• SPHERES

We consider the following nonlinear problem @@@ -Delta u + V (|y|)u = u(p), u > 0 in R-N, u is an element of H-1(R-N), (0.1) @@@ where V (r) is a positive function, 1 < p < N+2/N-2. We show that the multi-bump solutions constructed in [27] are non-degenerate in a suitable symmetric space. We also use this non-degenerate result to construct new solutions for (0.1).

• 单位
  清华大学