2024年4月26日星期五上午9：30-10：30

合肥工业大学 翡翠科教楼B1710

题目：Infinitely many Sign-changing normalized solutions of competition-diffusion p-Laplacian systems

报告摘要：In this talk, we are concerned with system of m p-Laplacian Schr\"odinger equations with competition interactions in a bounded regular domain. When the nonlinearities are odd satisfying some suitable assumptions, we can apply the vector genus and descending flow method to establish infinitely many sign-changing normalized solutions. The innovation is that we construct a tangent pseudo-gradient vector field for the energy functional on the constrained manifold, which can be used to find invariant sets of descending flow. The difficulty is reinforced by the p-Laplacian operator and also by the normalized constraint. Since we are dealing with $p>1$ in a unified way, the energy functional may be not regular enough and the p-Laplacian operator is not linear, we cannot benefit from certain classical techniques directly. This is a joint work with Prof. Jianjun Zhang and my students Anjie Feng and Jinfang Zhou.