一类液晶系统基态解和无穷多解的存在

Existence of Ground State Solutions and Infinitely Many Solutions for a Class of Liquid Crystal Systems

在这篇文章中,我们主要证明一类液晶系统基态解的存在性。在V和 g的假设下,我们利用Nehari流形的方法找到了这个解。之后,我们利用山路定理的方法证明了这类液晶系统非平凡解的存在性。最后我们对上述系统做了一些改进,利用亏格理论的方法证明了液晶系统的多重性结果,即证明了该系统无穷多解的存在性。

In this paper, we aim to prove the existence of ground state solutions for a class of liquid crystal system. Under the assumptions of V and the nonlinearity g, we find this solution using the Nehari manifold. After that, we prove the existence of nontrivial solutions of liquid crystal system by using the method of Mountain Pass Theorem. Finally, we have made some improvements, and prove a different type of multiplicity result by applying the Krasnoselskii genus theory, the existence of infinitely many solutions to the system.