In this paper, we deal with the Schrödinger’s problems, in the first part we study the theoretical side, we show the existence of at least three weak solutions, our main tools are based on variational inequalities, more precisely, using the three critical points theorem due to Ricceri, existence and multiplicity results are established. In the second part, we are interested in the application side, more exactly, we examine some computational problems on the discretization of finite elements of the p(x)-Laplacian, we propose a quasi-Newton minimization approach for the solution, our numerical tests show that these algorithms are able to resolve the problems with p(x)-Laplacian, for different values of p(x).

中文翻译：

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具有非标准p（x）增长条件的Schrödinger系统的存在性，多重性和数值示例

在本文中，我们解决了薛定ding的问题，在第一部分中，我们从理论上研究了至少三个弱解的存在，我们的主要工具是基于变分不等式的，更确切地说，是使用三个临界点定理由于Ricceri，存在和多重结果得以建立。在第二部分中，我们对应用程序侧感兴趣，更确切地说，我们研究了关于p（x）-Laplacian有限元离散化的一些计算问题，我们提出了一种拟牛顿最小化方法来求解测试表明，这些算法能够与解决问题的p（X）-Laplacian，对于不同的值p（x）。