A Trotter-Kato type result for a second order difference inclusion in a Hilbert space

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:361

Article

Apreutesei, N.¹  Apreutesei, G.² 

[1] Tech Univ Gh Asachi, Dept Math, Iasi 700506, Romania

[2] Alexandru Ioan Cuza Univ, Fac Math, Iasi 700506, Romania

关键词: Maximal monotone operator;    Strongly monotone operator;    The resolvent of an operator;    Yosida approximation;    Convergence in the sense of resolvent;   

DOI  :  10.1016/j.jmaa.2009.08.065

来源: Elsevier

【 摘 要 】

A Trotter-Kato type result is proved for a class of second order difference inclusions in a real Hilbert space. The equation contains a nonhomogeneous term f and is governed by a nonlinear operator A, which is supposed to be maximal monotone and strongly monotone. The associated boundary conditions are also of monotone type. One shows that, if A(n) is a sequence of operators which converges to A in the sense of resolvent and f(n) converges to f in a weighted l(2)-space, then under additional hypotheses, the sequence of the solutions of the difference inclusion associated to A(n) and f(n) is uniformly convergent to the solution of the original problem. (C) 2009 Elsevier Inc. All rights reserved.

【 授权许可】

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