In this paper, we prove the multiplicity of nontrivial solutions for a class of fractional-order elliptic equation with magnetic field. Under appropriate assumptions, firstly, we prove that the system has at least two different solutions by applying the mountain pass theorem and Ekeland’s variational principle. Secondly, we prove that these two solutions converge to the two solutions of the limit problem. Finally, we prove the existence of infinitely many solutions for the system and its limit problems, respectively.

中文翻译：

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可变增长变阶非线性分数阶磁性Schrödinger方程的多重性结果

在本文中，我们证明了带磁场的一类分数阶椭圆方程的非平凡解的多重性。在适当的假设下，首先，我们通过应用山口定理和Ekeland的变分原理证明系统具有至少两个不同的解决方案。其次，我们证明了这两个解都收敛到极限问题的两个解。最后，我们证明了该系统及其极限问题的无穷多个解的存在。