Abstract

We investigate a class of nonlinear singular integral equations with two monotone nonlinearities on the whole line. These equations have both theoretical and practical interest. We prove the existence theorem of a solution and the uniqueness theorem in a certain class of continuous and odd on \(\mathbb {R}\setminus\{0\}\) functions. The results of the work summarize some previously obtained research results in this direction. We find the limits of the solution of the equation at \(\pm\infty\). For obtained solution we investigate some its properties. We also establish the integral asymptotic for the constructed solutions. The results are illustrated by examples of the equations under consideration.

中文翻译：

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一类具有两个单调非线性的非线性积分方程在全线上的可解性

摘要

我们研究了一类在整行上具有两个单调非线性的非线性奇异积分方程。这些方程具有理论和实践意义。我们证明了\（\ mathbb {R} \ setminus \ {0 \} \）函数上某一类连续和奇数的解的存在性定理和唯一性定理。工作的结果总结了以前在这个方向上获得的一些研究结果。我们在\（\ pm \ infty \）找到方程解的极限。对于获得的解决方案，我们研究了其一些特性。我们还为构造的解建立了渐近积分。通过所考虑方程的示例来说明结果。