论文标题
非线性二阶不均匀微分方程在一个维度
Nonlinear second order inhomogeneous differential equations in one dimension
论文作者
论文摘要
我们研究了一个维度的非均匀非二阶微分方程。不均匀性可以是点源或连续的源分布。我们考虑$ ϕ'''（x） + v（ϕ（x））= q \，δ（x）$的二阶微分方程，其中$ v（ϕ）$是连续的，可分解的，分析函数和$ q \，Δ（x）$是点源。特别是我们研究表单$ v（ϕ（x））= a \，ϕ（x） + b \，ϕ^3（x）$的立方函数。我们表明，可以确定绿色功能以修改此类立方方程，并且该绿色功能可用于确定点源被连续源分布替换的情况的解决方案。
We study inhomogeneous nonlinear second-order differential equations in one dimension. The inhomogeneities can be point sources or continuous source distributions. We consider second order differential equations of type $ϕ''(x) + V(ϕ(x)) = Q \, δ(x) $, where $V(ϕ)$ is a continuous, differentiable, analytic function and $Q \,δ(x)$ is a point source. In particular we study cubic functions of the form $V(ϕ(x)) = A\,ϕ(x) + B\,ϕ^3(x)$. We show that Green functions can be determined for modifications of such cubic equations, and that such Green's functions can be used to determine the solutions for cases where the point source is replaced by a continuous source distribution.
