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Relaxation Results for Nonlinear Evolution Inclusions with One-sided Perron Right-hand Side

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Abstract

In a Banach space X, we study the evolution inclusion of the form x ′(t)∈A x(t)+F(t,x(t)), where A is an m-dissipative operator and F is an almost lower semicontinuous multifunction with nonempty closed values. If F is one-sided Perron with sublinear growth, then, we establish the relation between the solutions of the considered differential inclusion and the solutions of the relaxed one, i.e., \(x^{\prime} (t)\in Ax (t)+\overline{co}F (t,x (t) )\). A variant of the well known Filippov-Pliś lemma is also proved.

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Authors and Affiliations

  1. Department of Mathematics, Al. I. Cuza University, Iaşi, 700506, Romania

    Ovidiu Cârjă, Tzanko Donchev & Victor Postolache

  2. Octav Mayer Institute of Mathematics (Romanian Academy), Iaşi, 700505, Romania

    Ovidiu Cârjă

Authors
  1. Ovidiu Cârjă
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  2. Tzanko Donchev
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  3. Victor Postolache
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Correspondence to Ovidiu Cârjă.

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Cârjă, O., Donchev, T. & Postolache, V. Relaxation Results for Nonlinear Evolution Inclusions with One-sided Perron Right-hand Side. Set-Valued Var. Anal 22, 657–671 (2014). https://doi.org/10.1007/s11228-014-0284-5

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