二阶脉冲微分方程Dirichlet边值问题解的存在性  

Existence of Solutions for Second-Order Impulsive DifferentialEquations with Dirichlet Boundary Value Problems

作　　者：何婷 HE Ting(School of Mathematics and Statistics,Xidian University,Xi’an 710126,China)

机构地区：[1]西安电子科技大学数学与统计学院,西安710126

出　　处：《吉林大学学报（理学版）》2022年第3期475-480,共6页Journal of Jilin University:Science Edition

基　　金：国家自然科学基金(批准号:12061064).

摘　　要：用Leray-Schauder不动点定理,研究二阶脉冲微分方程Dirichlet边值问题-u″(x)+c(x)u(x)+∑p i=1 c iδ(x-x i)u(x)=h(x,u(x))+∑q j=1 h jδ(x-y j),x∈(0,1),u(0)=u(1)=0解的存在性,其中:c∈C([0,1],ℝ),h∈C([0,1]×ℝ,ℝ),c i,h j∈ℝ,i=1,2,…,p,j=1,2,…,q;p,q∈N;Diracδ-函数为当x≠0时,δ(x)=0,δ(0)=+∞,∫+∞-∞δ(x)d x=1;点0<x_(1)<x_(2)<…<x_(p)<1和0<y_(1)<y_(2)<…<y_(q)<1为给定的脉冲点.设存在p(·),q(·)∈L 2[0,1],使得h(x,u)≤q(x)+p(x)u,x∈[0,1],u∈ℝ.By using Leray-Schauder fixed point theorem, the author studies existence of solutions for second-order impulsive differential equations with Dirichlet boundary value problems -u″(x)+c(x)u(x)+∑ p i=1 c iδ(x-x i)u(x)=h(x,u(x))+∑ q j=1 h jδ(x-y j), x∈(0,1),u(0)=u(1)=0, where c∈C([0,1],ℝ), h∈C([0,1]×ℝ,ℝ), c i,h j∈ℝ, i=1,2,…,p, j=1,2,…,q;p,q∈N, the Dirac delta function δ(x) =0 when x≠0, δ(0)=+∞, ∫ +∞ -∞ δ(x) d x=1, points 0<x 1<x 2<…<x p<1 and 0<y 1<y 2<…<y q<1 are given impulse points. There exist p(·),q(·)∈L 2[0,1] such that h(x,u) ≤q(x)+p(x) u , x∈[0,1], u∈ℝ.

关 键 词：非线性微分方程 脉冲 LERAY-SCHAUDER不动点定理 DIRICHLET边值问题 

分 类 号：O175.8[理学—数学]