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

作者：Apreutesei N^*; Apreutesei G

来源：Journal of Mathematical Analysis and Applications, 2010, 361(1): 195-204.

DOI：10.1016/j.jmaa.2009.08.065

• Maximal monotone operator
• Strongly monotone operator
• The resolvent of an operator
• Yosida approximation
• Convergence in the sense of resolvent

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.

• 出版日期2010-1-1