A Trotter-Kato type result for a second order difference inclusion in a Hilbert space |
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Authors: | N Apreutesei G Apreutesei |
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Institution: | a Department of Mathematics, Technical Univ. “Gh. Asachi”, Iasi, 11, Bd. Carol I, 700506, Iasi, Romania b Faculty of Mathematics, Univ. “Al. I. Cuza”, Iasi, 11, Bd. Carol I, 700506, Iasi, Romania |
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Abstract: | 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 An is a sequence of operators which converges to A in the sense of resolvent and fn converges to f in a weighted l2-space, then under additional hypotheses, the sequence of the solutions of the difference inclusion associated to An and fn is uniformly convergent to the solution of the original problem. |
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Keywords: | Maximal monotone operator Strongly monotone operator The resolvent of an operator Yosida approximation Convergence in the sense of resolvent |
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