赵增勤,李宪奎.一类非线性积分方程正解的存在唯一性[J].数学研究及应用,1998,18(2):251~256 |
一类非线性积分方程正解的存在唯一性 |
On the Uniqueness and Existence of Positive Solution to a Class of Nonlinear Integral Equations |
投稿时间:1995-03-04 |
DOI:10.3770/j.issn:1000-341X.1998.02.019 |
中文关键词: 积分方程 摄动 正解 |
英文关键词:integral equation perturbation positive sotution. |
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中文摘要: |
本文研究积分方程u(x)=λ∫Ωk(x,y)f(y,u(y))dy,λ>0及其它的非线性摄动u(x)=λ∫Ωk(x,y)f(y,u(y))dy+G(u(x)),在k(x,y)非负可测,f(x,u),G(u)满足一定条件下,得到所述方程解的存在唯一性及其迭代逼近. |
英文摘要: |
We study the integral equationu(x)=λ∫Ωk(x,y)f(y,u(y))dy, λ>0 and its nonlinear perturbation u(x)=λ∫Ωk(x,y)f(y,u(y))dy+G(u(x)) where k(x,y) is nonnegative measurable. Under some reasonable conditions on f(x,u) and G(u) , we obtain the uniqueness and existence of positive solution for the equations, and also the iteration approximations of the solutions. |
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