The paper is devoted to the solvability questions of the Wiener-Hopf integral equation in the case where the kernel K satisfies the conditions 0 ≤ K ∈ L₁(ℝ), \(\int_{-\infty}^{\infty} K(t)dt>1\), K(±x) ∈ C⁽³⁾(ℝ⁺), (−1)ⁿK(±x)⁽ⁿ⁾(x) ≥ 0, x ∈ ℝ⁺, n =1, 2, 3. Based on Volterra factorization of the Wiener-Hopf operator, and invoking the technique of nonlinear functional equations, we construct real-valued solutions both for homogeneous and non-homogeneous Wiener-Hopf equations, assuming that the function g is real-valued and summable, and the corresponding conditions are satisfied. The behavior at infinity of the corresponding solutions is also studied.

纸张是专门用于维纳的Hopf积分方程的情况下的可解性问题，其中所述内核ķ满足条件0≤ ķ ∈大号₁（ℝ），\（\ INT _ { - \ infty} ^ {\ infty} K和（吨）DT> 1 \） ，ķ（± X）∈ ç ^（3）（ℝ ⁺），（ - 1）^ñ K（± X）^（ñ）（X）≥0，X ∈ℝ ⁺，ñ= 1，2，3。基于Wiener-Hopf算子的Volterra分解，并调用非线性泛函方程技术，我们假设函数g为均质和非均质Wiener-Hopf方程，构造实值解。是实值且可求和，并且满足相应条件。还研究了相应解的无穷大行为。