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The method of lower and upper solutions for impulsive fractional evolution equations in Banach spaces

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In this paper, we investigate the existence of mild solutions for a class of fractional impulsive evolution equation with periodic boundary condition by means of the method of upper and lower solutions and monotone iterative method. Using the theory of Kuratowski measure of noncompactness, a series of results about mild solutions are obtained. Finally, two examples are given to illustrate our results.

Abstract

In this paper, we investigate the existence of mild solutions for a class of fractional impulsive evolution equation with periodic boundary condition by means of the method of upper and lower solutions and monotone iterative method. Using the theory of Kuratowski measure of noncompactness, a series of results about mild solutions are obtained. Finally, two examples are given to illustrate our results.

참고문헌 (33)

  1. R. P. Agarwal, "A survey on existence results for boundary value problems of nonlinear fractional dierential equations and inclusions", Acta Appl. Math, 109(3), pp.973~1033 (2010)[DOI]
  2. A. Aghajani, "Some generalizations of Darbo xed point the-orem and applications", Bull. Belg. Math. Soc. Simon Stevin, 20(2), pp.345~358 (2013)
  3. B. Ahmad, "Existence results for nonlinear impulsive hybrid bound-ary value problems involving fractional dierential equations", Nonlinear Anal. Hybrid Syst, 3(3), pp.251~258 (2009)[DOI]
  4. Z. Bai, "Existence results for impulsive nonlinear fractional dif-ferential equation with mixed boundary conditions", Bound. Value Probl., 2016 (2016)[DOI]
  5. K. Balachandran, "Existence of solutions of abstract fractional impulsive semilinear evolution equations", Electron. J. Qual. Theory Dier. Equ, 2010(4), pp.12~ (2010)[DOI]
  6. J. Banas, "Measures of noncompactness in Banach spaces", Lecture Notes in Pure and Applied Mathematics, 60 (1980), Marcel Dekker, Inc
  7. M. Benchohra, "Contemporary Mathematics and Its Applications, 2" (2006), Hindawi Publishing Cor-poration
  8. M. Benchohra, "Impulsive fractional dierential equations in Banach spaces", Electron. J. Qual. Theory Dier. Equ, 2009(8), pp.14~ (2009)[DOI]
  9. P. Chen, "Mixed monotone iterative technique for a class of semilinear impul-sive evolution equations in Banach spaces", Nonlinear Anal, 74(11), pp.3578~3588 (2011)[DOI]
  10. P. Chen, "On the initial value problem of fractional evolution equations with noncompact semigroup", Comput. Math. Appl, 67(5), pp.1108~1115 (2014)[DOI]
  11. S. W. Du, "Monotone iterative technique for dierential equa-tions in a Banach space", J. Math. Anal. Appl, 87(2), pp.454~459 (1982)[DOI]
  12. M. Feckan, "On the concept and existence of solution for impul-sive fractional dierential equations", Commun. Nonlinear Sci. Numer. Simul, 17(7), pp.3050~3060 (2012)[DOI]
  13. D. J. Guo, "Nonlinear problems in abstract cones, Notes and Reports in Mathematics in Science and Engineering, 5" (1988), Academic Press, Inc
  14. Ordinary Dierential Equations in Abstract Spaces, "D. J. Guo", Shandong Science and Technology, ~ (1989)
  15. H. -P. Heinz, "On the behaviour of measures of noncompactness with respect to dier-entiation and integration of vector-valued functions", Nonlinear Anal, 7(12), pp.1351~1371 (1983)[DOI]
  16. H. Lakzian, "New xed point results for mappings of contractive type with an application to nonlinear fractional dierential equations", J. Fixed Point Theory Appl, 18(2), pp.251~266 (2016)[DOI]
  17. B. Li, "Monotone iterative method for the periodic boundary value problems of impulsive evolution equations in Banach spaces", Chaos Solitons Fractals, 110, pp.209~215 (2018)[DOI]
  18. Y. Li, "Positive solutions of abstract semilinear evolution equations and their applica-tions", Acta Math. Sinica (Chin. Ser.), 39(5), pp.666~672 (1996)
  19. J. Mu, "Extremal mild solutions for impulsive fractional evolution equations with nonlocal initial conditions", Bound. Value Probl, 2012, pp.71~ (2012)[DOI]
  20. J. Mu, "Monotone iterative technique for impulsive fractional evolution equa-tions", J. Inequal. Appl, 125, pp.12~ (2011)[DOI]
  21. A. Pazy, "Semigroups of linear operators and applications to partial dierential equations", Applied Mathematical Sciences, 44 (1983), Springer-Verlag
  22. X. -B. Shu, "The existence and uniqueness of mild solutions for fractional dierential equations with nonlocal conditions of order 1 < < 2", Comput. Math. Appl, 64(6), pp.2100~2110 (2012)[DOI]
  23. J. X. Sun, "Extremal solutions of initial value problem for integro-dierential equations of mixed type in Banach spaces", Ann. Dierential Equations, 8(4), pp.469~475 (1992)
  24. G. Wang, "Comments on the concept of existence of solution for impulsive fractional dierential equations", Commun. Nonlinear Sci. Numer. Simul, 19(3), pp.401~403 (2014)[DOI]
  25. G. Wang, "Systems of rst order impulsive functional dierential equations with deviating arguments and nonlinear boundary conditions", Nonlinear Anal, 74(3), pp.974~982 (2011)[DOI]
  26. J. Wang, "On the new concept of solutions and existence results for impulsive fractional evolution equations", Dyn. Partial Dier. Equ, 8(4), pp.345~361 (2011)[DOI]
  27. J. Wang, "Ulam's type stability of impulsive ordinary dierential equations", J. Math. Anal. Appl, 395(1), pp.258~264 (2012)[DOI]
  28. J. Wang, "On the natural solution of an impulsive fractional dier-ential equation of order q 2 (1; 2)", Commun. Nonlinear Sci. Numer. Simul, 17(11), pp.4384~4394 (2012)[DOI]
  29. J. Wang, "Alternative results and robustness for fractional evolution equations with periodic boundary conditions", Electron. J. Qual. Theory Dier. Equ, 2011(97), pp.15~ (2011)[DOI]
  30. J. Wang, "On recent developments in the theory of boundary value problems for impulsive fractional dierential equations", Comput. Math. Appl, 64(10), pp.3008~3020 (2012)[DOI]
  31. J. Wang, "Abstract Cauchy problem for fractional dierential equations", Nonlinear Dy-nam, 71(4), pp.685~700 (2013)[DOI]
  32. H. Ye, "A generalized Gronwall inequality and its application to a fractional dierential equation", J. Math. Anal. Appl, 328(2), pp.1075~1081 (2007)[DOI]
  33. W. -X. Zhou, "Existence of solutions for fractional dierential equations with multi-point boundary conditions", Commun. Nonlinear Sci. Numer. Simul., 17(3), pp.1142~1148 (2012)[DOI]

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