We consider a system of nonlinear integral equations arising when studying the inverse coefficient problem for a system of partial differential equations. The inverse problem is to determine two coefficients of the system based on additional information on one of the solution components. We prove the local existence and uniqueness of the solution of the nonlinear system of integral equations and, as a consequence, the existence and uniqueness of the solution of the inverse problem.

中文翻译：

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非线性积分方程组解的存在唯一性

我们考虑在研究偏微分方程组的反系数问题时出现的非线性积分方程组。逆问题是根据解分量之一的附加信息确定系统的两个系数。我们证明了非线性积分方程组解的局部存在唯一性，从而证明了反问题解的存在唯一性。