非线性Schrodinger方程是量子理论中的重要方程，近几十年来，引起了众多物理学家和数学家的关注。由于波函数的内在性质，很自然地会要求方程的解满足正规化条件，得到的解也就称为正规化解。从物理的角度来说，研究Schrodinger方程的正规化解更有意义。本文主要通过变分法来研究某些非线性Schrodinger方程以及Schrodinger类型的方程组，得到正规化解的存在性与多重性等结果。 具体说来，在质量次临界的情形，本文将研究同时带有位势项与非自治项的Schrodinger方程。其中，位势项只需满足基本的连续性假设，而非自治的非线性项只需满足几乎最优的 Berestycki-Lions 类型条件，以及一个比 Ambrosetti-Rabinowitz 条件还弱的技术性假设。在这些条件下，本文将证明非线性Schrodinger方程基态解的存在性和径向对称正规化解的多重性。这似乎是在正规化解方面，位势项和非自治项同时存在时的第一个结果。并且，这些方法还可以应用到其他Schrodinger类型的方程上去。 另外，在质量超临界的情形，本文将对法国数学家Jeanjean在文献（Nonlinear Anal., 1997）中的结果给出新的证明。在原始文献中，Jeanjean利用辅助泛函构造了满足额外条件的 Palais-Smale 序列，然后通过巧妙的紧性分析证明了Schrodinger方程存在基态解。本文将引进一种新的方法，先证明能量泛函在Pohozaev流形上的极小值连续依赖于正规化条件，并且该极小值关于正规化条件是严格递减的，然后通过这一性质来证明该极小值可达，从而证明基态解存在。 本文还将经典Schrodinger方程组正规化解方面的部分结果，推广到Kirchhoff方程组上去。这是一类非局部的方程，因此在证明过程中，除了要考虑经典Schrodinger方程组将面临的难点，还需解决非局部项带来的困难。在质量次临界时，已有部分结果，因此本文将继续考虑质量超临界情形和混合情形。在质量超临界的情形，本文将进一步发展Jeanjean的方法，构造有界的 Palais-Smale 序列，并证明该序列存在强收敛的子列，从而证明了基态解存在。而对于混合情形，本文将对方程组的Pohozaev 流形进行分解，证明能量泛函存在局部极小值点，并且该局部极小还是基态解。

The nonlinear Schrodinger equation is an important equation in quantum theory that has attracted the attention of many physicists and mathematicians in recent decades. Due to the intrinsic nature of the wave function, it is natural to require the solution of the equation to satisfy the normalization condition, and so the solution obtained is called the normalized solution. From the physical point of view, it is more meaningful to study the normalized solutions of Schrodinger equations. In this paper, we will study some nonlinear Schrodinger equations and Schrodinger-type systems by variational methods to obtain the existence and multiplicity of normalized solutions.More specifically, in the mass subcritical case, we will study nonlinear Schrodinger equations with both potential and non-autonomous terms. In this paper, the potentials are required to satisfy only the basic continuity assumptions, while the non-autonomous nonlinearities only need to satisfy the Berestycki-Lions type conditions which are almost optimal and a technical assumption that is weaker than the Ambrosetti-Rabinowitz condition. Under these conditions, we will prove the existence of ground state solutions and the multiplicity of radially symmetric normalized solutions to the nonlinear Schrodinger equations. This seems to be the first result in terms of normalized solutions when both potentials and non-autonomous nonlinearities are present. Moreover, these methods can be applied to other equations of Schrodinger-type.Furthermore, in the mass supercritical case, we will give a new proof of the result of the French mathematician Jeanjean in (Nonlinear Anal., 1997). In the original paper, Jeanjean constructed a Palais-Smale sequence satisfying additional conditions using auxiliary functional, and then proved the existence of ground state solutions to the Schrodinger equation by brilliant analysis. In this paper, we will introduce a new approach by first proving that the minimal value of the energy functional on the Pohozaev manifold depends continuously on the normalized condition and that the minimal value is strictly decreasing with respect to the normalized condition, and then proving that the minimal value is obtainable by this property, thus proving the existence of the ground state solution.In this paper, we also extend some of the results on the normalized solutions of classical Schrodinger systems to the Kirchhoff systems. This is a non-local class of equations, so in the course of the proof, in addition to the difficulties that will be faced by classical Schrodinger systems, it is necessary to address the difficulties posed by the non-local terms. Partial results are available in the mass subcritical case, so we will continue to consider the mass supercritical case and the mixed case. In the mass supercritical case, we will further develop the method of Jeanjean by constructing a bounded Palais-Smale sequence and proving that the sequence has a strongly convergent subsequence, thus proving the existence of the ground state solution. For the mixed case, we will decompose the Pohozaev manifold of the system and prove that there is a local minima of the energy functional and that the local minima is still a ground state solution.