The aim of this paper is to present the new existence criteria for the nonlinear algebraic system with the indefinite coefficient matrix. By imposing the symmetric conditions on the nonlinear term related to the eigenvalues of the algebraic system at zero and infinity, respectively, the existence results of multiple solutions are established. The methods employed are variational approach.

中文翻译：

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具有不定系数矩阵的非线性代数系统的多重解

本文的目的是提出具有不确定系数矩阵的非线性代数系统的新存在准则。通过将对称条件施加于与代数系统特征值分别为零和无穷大的非线性项上，建立了多个解的存在性结果。所采用的方法是可变方法。