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Acta Mathematica Scientia, 1988
We obtain some results about the convergence of solutions of the boundary value problems of the third order nonlinear ordinary differential equation with a small parameter \(\epsilon >0:\) (1) \(\epsilon x\prime''=f(t,x,x',x'',\epsilon)\), \((2_ i)\) \(x^{(i)}(0)=0\), \(x(1)=0\), \(x'(1)=0\) \((i=0,1,2)\) to a solution of their reduced problem \(u ...
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We obtain some results about the convergence of solutions of the boundary value problems of the third order nonlinear ordinary differential equation with a small parameter \(\epsilon >0:\) (1) \(\epsilon x\prime''=f(t,x,x',x'',\epsilon)\), \((2_ i)\) \(x^{(i)}(0)=0\), \(x(1)=0\), \(x'(1)=0\) \((i=0,1,2)\) to a solution of their reduced problem \(u ...
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SIAM Journal on Mathematical Analysis, 1984
Asymptotic integration of a linear differential equation \[ x^{(n)}+[a_ 1+p_ 1(t)]x^{(n-1)}+...+[a_ n+p_ n(t)]x=0 \] is considered under conditions that the integrals \(\int^{\infty}p_ k(t)e^{ct}t^ qdt\) (where c and q are nonnegative constants) converge (perhaps relatively).
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Asymptotic integration of a linear differential equation \[ x^{(n)}+[a_ 1+p_ 1(t)]x^{(n-1)}+...+[a_ n+p_ n(t)]x=0 \] is considered under conditions that the integrals \(\int^{\infty}p_ k(t)e^{ct}t^ qdt\) (where c and q are nonnegative constants) converge (perhaps relatively).
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Journal of Mathematical Sciences, 2019
Consider the two-dimensional system of singularly perturbed differential equations \[\begin{aligned}\varepsilon^2\frac{d^2u}{dx^2} & =h(x)(u-\varphi(v,x))^2-\varepsilon F_1(u,v,x,\varepsilon), \\ \varepsilon\frac{d^2v}{dx^2} & =f(u,v,x,\varepsilon)\end{aligned} \tag{1}\] on the interval \([0,1]\) with the boundary conditions \[u(0,\varepsilon)=u^0,\ u ...
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Consider the two-dimensional system of singularly perturbed differential equations \[\begin{aligned}\varepsilon^2\frac{d^2u}{dx^2} & =h(x)(u-\varphi(v,x))^2-\varepsilon F_1(u,v,x,\varepsilon), \\ \varepsilon\frac{d^2v}{dx^2} & =f(u,v,x,\varepsilon)\end{aligned} \tag{1}\] on the interval \([0,1]\) with the boundary conditions \[u(0,\varepsilon)=u^0,\ u ...
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Colloidal Self-Assembly Approaches to Smart Nanostructured Materials
Chemical Reviews, 2022Zhiwei Li Li, Yadong Yin
exaly
New Creatinine- and Cystatin C–Based Equations to Estimate GFR without Race
New England Journal of Medicine, 2021Lesley A Inker +2 more
exaly
PERTURBATION OF INVARIANT MANIFOLDS OF ORDINARY DIFFERENTIAL EQUATIONS
1996GEORGE OSIPENKO, EUGENE ERSHOV
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Benchmarking the performance of all-solid-state lithium batteries
Nature Energy, 2020Dominik A Weber +2 more
exaly
Singular perturbations of difference methods for linear ordinary differential equations
Applicable Analysis, 1980Hans-Jurgen Reinhardt +4 more
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