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    非線性非局部初值的發(fā)展方程解的存在性

    2017-10-23 23:09:18譚錦梅
    學(xué)習(xí)導(dǎo)刊 2017年3期

    譚錦梅

    摘 要:在Banach空間,利用非線性泛函分析中的不動(dòng)點(diǎn)理論,并在一定的假設(shè)下,對(duì)帶有初始問(wèn)題的非線性發(fā)展方程解的存在性進(jìn)行研究。

    關(guān)鍵詞:凝聚映射,非線性發(fā)展方程,非局部初值

    中圖分類號(hào): 文獻(xiàn)標(biāo)識(shí)碼:A

    0 引言

    隨著科學(xué)技術(shù)的發(fā)展,非局部抽象柯西問(wèn)題解的存在性已在很多文章中被深入研究過(guò)。非局部抽象柯西問(wèn)題它在物理、經(jīng)濟(jì)、通訊等領(lǐng)域都有著廣泛的應(yīng)用前景;同時(shí),研究方法涉及到泛函分析、常微分方程、偏微分方程等基礎(chǔ)數(shù)學(xué)理論,有著廣泛的理論意義。帶非局部初值的初值問(wèn)題最早是在Byszweki[1]提出來(lái)的,后來(lái)許多學(xué)者利用不同的不動(dòng)點(diǎn)定理證明其解的存在性。本文通過(guò)定義映射,用兩個(gè)不動(dòng)點(diǎn)定理的引理來(lái)證明其解在Banach空間中的存在性。

    參考文獻(xiàn):

    [1] L. Byszewski, Theorems about the existence and uniqueness of solutions of a semilinear evolution nonlocal Cauchy problem[J].J Math Anal Appl,1991,(162): 494–505.

    [2] S. Aizicovici, M. McKibben, Existence results for a class of abstract nonlocal Cauchy problems[J].Nonlinear Anal,2000,(39):649–668.

    [3] J. Liang, T.J. Xiao, Semilinear integrodifferential equations with nonlocal initial conditions[J].Comput Math Appl,2004,(47):863–875.

    [4] Y. Chen. Anti-periodic solutions for semilinear evolution equations[J].J Math Anal Appl,2006,(315):337–348.

    [5] L.P. Zhu, G. Li, Nonlocal differential equations with multivalued perturbations in Banach spaces[J].Nonlinear Anal,2008,(69):2843–2850.

    [6] J. Garcia-Falset, Existence results and asymptotic behavior for nonlocal abstract Cauchy problems[J]. J Math Anal Appl,2008,(338):639–652.

    [7] Liu, Q. and Yuan, R., Existence of mild solutions for semilinear evolution equations with nonlocal initial conditions[J].Nonlin Anal,2009,(71):4177–4184.

    [8] Zeidler, E.Nonlinear Functional Analysis and Its Applications II[M].New York:Springer,1990.

    [9] W.V.Petryshyn,Structure of the fixed points sets of k-set-contractions[J]. Arch Ration Mech Anal,970/1971,(40):312–328

    [10] Ph. Bénilan, Equations d'evolution dans un espace de Banach quelconque et applications, Thèse de doctorat d'?tat, Orsay, 1972.

    Existence result for nonlinear evolution equations with non-local initial conditions

    TAN Jin Mei

    (South China University of Technology,Guangzhou 510641,China)

    Abstract: In Banach space,Using Leray-Schauders topology degree theory in a nonlinear functional analysis, and under certain assumptions,it studies existence result for nonlinear evolution equations with the initial conditions.

    Key Words: Leray-Schauder degree;nonlinear evolution equations;nonlocal initial condition;endprint

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