The impulsive solution for a semi-linear singularly perturbed differential-difference equation is studied. Using the methods of boundary function and fractional steps, we construct the formula asymptotic expansion of ...The impulsive solution for a semi-linear singularly perturbed differential-difference equation is studied. Using the methods of boundary function and fractional steps, we construct the formula asymptotic expansion of the problem. At the same time, Based on sewing techniques, the existence of the smooth impulsive solution and the uniform validity of the asymptotic expansion are proved.展开更多
研究了一类具有连续分布滞量含阻尼项的非线性双曲型偏微分方程~2u(x,t)/t^2+p(t)u(x,t)/t+A(x,t)u(x,t)+sum from i=1 to m_1( )∫_a^bB_i(x,t,τ)f_i(u(x,r_1(t,τ)))dm(τ)=C(t)Δu(x,t)+sum from j=1 to m_2( )∫_a^bD_j(t,...研究了一类具有连续分布滞量含阻尼项的非线性双曲型偏微分方程~2u(x,t)/t^2+p(t)u(x,t)/t+A(x,t)u(x,t)+sum from i=1 to m_1( )∫_a^bB_i(x,t,τ)f_i(u(x,r_1(t,τ)))dm(τ)=C(t)Δu(x,t)+sum from j=1 to m_2( )∫_a^bD_j(t,τ)Δu(x,r2(t,τ))dm(τ),获得了该方程在两类边值条件下解振动的充分条件.展开更多
基金Supported by the National Natural Science Foundation of China(N.11501236,N.11471118,N.30921064 and 90820307),the Innovation Project in the Chinese AcademDepartment of Mathematics,Shanghai Key Laboratory of PMMP,East China Normal University
文摘The impulsive solution for a semi-linear singularly perturbed differential-difference equation is studied. Using the methods of boundary function and fractional steps, we construct the formula asymptotic expansion of the problem. At the same time, Based on sewing techniques, the existence of the smooth impulsive solution and the uniform validity of the asymptotic expansion are proved.
文摘研究了一类具有连续分布滞量含阻尼项的非线性双曲型偏微分方程~2u(x,t)/t^2+p(t)u(x,t)/t+A(x,t)u(x,t)+sum from i=1 to m_1( )∫_a^bB_i(x,t,τ)f_i(u(x,r_1(t,τ)))dm(τ)=C(t)Δu(x,t)+sum from j=1 to m_2( )∫_a^bD_j(t,τ)Δu(x,r2(t,τ))dm(τ),获得了该方程在两类边值条件下解振动的充分条件.
