We study the existence and uniqueness as well as the asymptotic behaviour of solutions of a certain boundary-value problem for a convolution integral equation on the whole line with monotone non-linearity. In some special cases, there are concrete applications to ##IMG## [http://ej.iop.org/images/1064-5632/84/4/807/IZV_84_4_807ieqn1.gif] {$p$} -adic string theory, the mathematical theory of the geographical spread of an epidemic, the kinetic theory of gases and the theory of radiation transfer. We prove the existence and uniqueness of an odd bounded continuous solution. The monotonicity and the integral asymptotics of this solution is also discussed. We finally give particular application-oriented examples of the equations considered, which illustrate the special nature of our results.

中文翻译：

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单调非线性卷积积分方程一个边值问题解的存在唯一性

我们研究了具有单调非线性的全线上卷积积分方程的一个边值问题的解的存在性和唯一性以及其渐近性。在某些特殊情况下，## IMG ##有具体的应用[http://ej.iop.org/images/1064-5632/84/4/807/IZV_84_4_807ieqn1.gif] {$ p $} -adic string理论，流行病地理扩散的数学理论，气体动力学理论和辐射传输理论。我们证明了奇有界连续解的存在性和唯一性。还讨论了该解决方案的单调性和积分渐近性。最后，我们给出所考虑方程式的特定于应用程序的示例，这些示例说明了我们结果的特殊性质。