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Let A be a set, and let E be the Banach space of bounded functions : A R, equipped with its natural order. With a rectangle R = (a,b) × (0,T] let F(x,t,) : R × E E be a bounded, continuous function satisfying a local Hölder condition and being quasimonotone increasing with respect to . Then there exists a solution u: [a,b] × [0,T] E of the problem ut(x,t) – uxx(x,t) = F(x,t,u(x,t)) ((x,t) R), u(x,t) = 0 ((x,t) R R). 相似文献
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In this paper we first develop a theory of almost automorphic
functions with values in Frechet spaces. Then, we consider the
semilinear differential equation x'(t) = A x(t) + f(t, x(t)), t ∈ ℝ in a Frechet space X, where A is the infinitesimal generator
of a C0-semigroup satisfying some conditions of exponential stability. Under suitable conditions on f, we prove the existence and
uniqueness of an almost automorphic mild solution to the equation. 相似文献
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中立型时滞微分方程的振动性 总被引:14,自引:1,他引:14
本文讨论一类一阶中立型时滞微分方程的振动性,建立了此类方程一切解振动的几族充分条件,作为其推论的结果改进了文[1],[2],[3]的相应定理。 相似文献
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Tassilo KüpperRong Yuan 《Journal of Mathematical Analysis and Applications》2002,267(1):173-193
We study the existence of quasi-periodic solutions to differential equations with piecewise constant argument (EPCA, for short). It is shown that EPCA with periodic perturbations possess a quasi-periodic solution and no periodic solution. The appearance of quasi-periodic rather than periodic solutions is due to the piecewise constant argument. This new phenomenon illustrates a crucial difference between ODE and EPCA. The results are extended to nonlinear equations. 相似文献
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该文得到中立型线微分方程组d/dt[x(t)-x(t-τ)] A(t)x(t-σ(t))=0全体非平凡解振动充分条件的代数判别准则。 相似文献
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考虑二阶脉冲微分方程(r(t)(x′(t))σ)′+f(t,x(t),x′(t))=0,t t0,t≠tk,k=1,2,…x(tk+)=gk(x(tk)),x′(tk+)=hk(x′(tk)),k=1,2,…(E)其中0 t0相似文献
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本文利用Riccati技巧和平均技巧,研究一类二阶非线性微分方程的振动性,得到了这类方程振动的若干新的判别准则。 相似文献
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OscillationsofSecondOrderNonlinearNeutralDifferentialEquationsWandOiru;(王其如)WuYewei(武业伟)(LuogangTeachers'College,Luoyang47102... 相似文献
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非线性二阶中立型微分方程的振动性 总被引:10,自引:0,他引:10
考虑中立型微分方程我们建立了方程(1)的若干振动准则。这些结果适用于强超线性和强次线性中立型微分方程,且当p(t)≡0时仍然成立。 相似文献
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研究奇数阶混合中立型微分方程[x(t)+ax(t-τ)-bx(t+σ)](n)+δ(qx(t-g)+px(t+h))=0其中a,b,q,p,τ,σ,g,h为正常数,δ=±1,n为奇数.得到方程若干新的振动定理,改进和推广了文[1]中的结果. 相似文献
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本文研究一类二阶不稳定型非线性中立型微分方程,得到了该类方程解振动的充分条件. 相似文献
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本文讨论一类多滞量中立抛物型偏微分方程解的振动性质 ,获得了其一切解振动的充分条件 ;指出了与普通抛物型偏微分方程质的差异 . 相似文献
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In this article, we study conditions for the asymptotic equivalence of differential equations in Hilbert spaces. We also discuss
the relationship between the properties of solutions of differential equations of triangular form and those of truncated differential
equations.
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Published in Ukrains'kyi Matematychnyi Zhurnal, Vol. 57, No. 3, pp. 329–337, March, 2005. 相似文献
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Abdullayev F. G. Bushev D. M. kyzy M. Imash Kharkevych Yu. I. 《Ukrainian Mathematical Journal》2020,71(8):1153-1172
Ukrainian Mathematical Journal - We determine the subspaces of solutions of the systems of Laplace and heat-conduction differential equations isometric to the corresponding spaces of real functions... 相似文献