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Applicable Analysis
An International Journal
Volume 96, 2017 - Issue 15
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Original Articles

Nonlocal semilinear integro-differential inclusions via vectorial measures of noncompactness

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Pages 2526-2544 | Received 03 Jun 2016, Accepted 17 Aug 2016, Published online: 01 Sep 2016

References

  • Cardinali T, O’Regan D, Rubbioni P. Mönch sets and fixed point theorems for multimaps in locally convex topological vector spaces. Fixed Point Theory, Forthcoming.
  • Kamenskii M, Obukhovskii V, Zecca P. Condensing multivalued maps and semilinear differential inclusions in Banach spaces. Vol. 7, De Gruyter Ser. Nonlinear Anal. Appl., Berlin: Walter de Gruyter; 2001.
  • Andres J, Malaguti L, Pavlacková M. On second-order boundary value problems in Banach spaces: a bound sets approach. Topol. Methods Nonlinear Anal. 2011;37:303–341.
  • Pazy A. Semigroups of linear operators and applications to partial differential equations. Berlin: Springer-Verlag; 1983.
  • Ahmad B, Malar K, Karthikeyan K. A study of nonlocal problems of impulsive integrodifferential equations with measure of noncompactness. Adv. Differ. Equ. 2013;2013:205, 11 pp.
  • Benedetti I, Malaguti L, Taddei V. Semilinear evolution equations in abstract spaces and applications. Rend. Istit. Mat. Univ. Trieste. 2012;44:371–388.
  • Benedetti I, Obukhovskii V, Taddei V. Controllability for systems governed by semilinear evolution inclusions without compactness. NoDEA Nonlinear Differ. Equ. Appl. 2014;21:795–812.
  • Cardinali T, Rubbioni P. Impulsive mild solutions for semilinear differential inclusions with nonlocal conditions in Banach spaces. Nonlinear Anal. 2012;75:871–879.
  • Malaguti L, Rubbioni P. Nonsmooth feedback controls of nonlocal dispersal models. Nonlinearity. 2016;29:823–850. doi:10.1088/0951-7715/29/3/823
  • Martin RH Jr, Smith HL. Reaction--diffusion systems with time delays: monotonicity, invariance, comparison and convergence. J. Reine Angew. Math. 1991;413:1–35.
  • Liang D, Wu J. Travelling waves and numerical approximations in a reaction advection diffusion equation with nonlocal delayed effects. J. Nonlinear Sci. 2003;13:289–310.
  • Ou C, Wu J. Persistence of wavefronts in delayed nonlocal reaction--diffusion equations. J. Differ. Equ. 2007;235:219–261.
  • Zhao Z, Rong E. Reaction diffusion equation with spatio-temporal delay. Commun. Nonlinear Sci. Numer. Simul. 2014;19:2252–2261.
  • Cardinali T, Rubbioni P. On the existence of mild solutions of semilinear evolution differential inclusions. J. Math. Anal. Appl. 2005;308:620–635.
  • Cardinali T, Rubbioni P. Corrigendum and addendum to “On the existence of mild solutions of semilinear evolution differential inclusions” [J. Math. Anal. Appl. 308 (2005), no. 2, 620--635]. J. Math. Anal. Appl. 2016;438:514–517. doi:10.1016/j.jmaa.2016.01.066
  • Cardinali T, Rubbioni P. Multivalued fixed point theorems in terms of weak topology and measure of weak noncompactness. J. Math. Anal. Appl. 2013;405:409–415.
  • Heuser HG. Functional analysis. John Horvath, translator; A Wiley-Interscience Publication, Chichester: John Wiley & Sons Ltd; 1982. German.
  • O’Regan D, Precup R. Existence criteria for integral equations in Banach spaces. J. Inequal. Appl. 2001;6:77–97.
  • Heinz HP. On the behaviour of measures of noncompactness with respect to differentiation and integration on vector-valued functions. Nonlinear Anal. 1983;7:1351–1371.
  • Lizama C, Pozo JC. Existence of mild solutions for a semilinear integrodifferential equation with nonlocal initial conditions. Abstr. Appl. Anal. 2012;2012:15 pp.
  • Fan Z, Dong Q, Li G. Semilinear differential equations with nonlocal conditions in Banach spaces. Int. J. Nonlinear Sci. 2006;2:131–139.
  • Xue X. Semilinear nonlocal differential equations with measure of noncompactness in Banach spaces. Nanjing Daxue Xuebao Shuxue Bannian Kan. 2007;24:264–276.
  • Denkowski Z, Migórski S, Papageorgiou NS. An introduction to nonlinear analysis: theory. Boston (MA): Kluwer Academic Publishers; 2003.
  • Zeidler E. Nonlinear functional analysis and its applications. I. Fixed-point theorems. New York (NY): Springer-Verlag; 1986.

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