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Existence results for a class of second order evolution inclusions and its corresponding first order evolution inclusions

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Abstract

We deal with an abstract second order nonlinear evolution inclusion with its principal part having a small parameter ɛ. We prove the existence of a weak solution when the nonlinearity F is convex as well as nonconvex valued. Then we study the asymptotic behavior of a sequence of solutions {u ɛ } when ɛ → 0. We prove that there exists a limit function u, and u is a solution of the corresponding first order evolution inclusion.

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Authors and Affiliations

  1. School of Science, Guangxi University for Nationalities Nanning, 530006, Guangxi Province, P. R. China

    Xiaoyou Liu & Zhenhai Liu

  2. School of Mathematical Science and Computing Technology, Central South University Changsha, 410075, Hunan Province, P.R. China

    Xiaoyou Liu & Zhenhai Liu

Authors
  1. Xiaoyou Liu
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  2. Zhenhai Liu
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Correspondence to Zhenhai Liu.

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Supported by NNSF of China Grant No. 10971019.

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Liu, X., Liu, Z. Existence results for a class of second order evolution inclusions and its corresponding first order evolution inclusions. Isr. J. Math. 194, 723–743 (2013). https://doi.org/10.1007/s11856-012-0092-2

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  • DOI: https://doi.org/10.1007/s11856-012-0092-2

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