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Tytuł artykułu

Monotone iterative technique for non-autonomous semilinear differentia equations with nonlocal condition

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Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
The objective of this article is to discuss the existence and uniqueness of mild solutions for a class of non-autonomous semilinear differential equations with nonlocal condition via monotone iterative method with upper and lower solutions in an ordered complete norm space X, using evolution system and measure of noncompactness.
Wydawca
Rocznik
Strony
29--39
Opis fizyczny
Bibliogr. 26 poz.
Twórcy
autor
  • Indian Institute of Technology Roorkee, India
  • Indian Institute of Technology Roorkee, India
Bibliografia
  • [1] Byszewski L., Theorem about the existence and uniqueness of solutions of a semilinear evolution nonlocal Cauchy problem, J. Math. Anal. Appl., 1991, 162(2), 494–505
  • [2] Deng K., Exponential decay of solutions of semilinear parabolic equations with nonlocal initial conditions, J. Math. Anal. Appl., 1993, 179(2), 630–637
  • [3] Chen P., Zhang X., Li Y., Approximation technique for fractional evolution equations with nonlocal integral conditions, Mediterr. J. Math., 2017, 14(6), 226
  • [4] Du S., Lakshmikantam V., Monotone iterative technique for differential equation in a Banach space, J. Math. Anal. Appl., 1982, 87(2), 454–459
  • [5] Chen P., Li Y., Monotone iterative technique for a class of semilinear evolution equations with nonlocal conditions, Results Math., 2013, 63(3-4), 731–744
  • [6] Chen P., Mu J., Monotone iterative method for semilinear impulsive evolution equations of mixed type in Banach space, Electron. J. Differ. Equ., 2010, 149, 1–13
  • [7] Mu J., Monotone iterative technique for fractional evolution equations in Banach spaces, J. Appl. Math., 2011, Article ID 767186, DOI: 10.1155/2011/767186
  • [8] Mu J., Li Y., Monotone iterative technique for impulsive fractional evolution equations, J. Inequal. Appl., 2011, 125, 1–12
  • [9] Chen P., Li Y., Yang H., Perturbation method for nonlocal impulsive evolution equations, Nonlinear Anal. Hybrid Syst., 2013, 8, 22–30
  • [10] Chen P., Li Y., Existence of mild solutions for fractional evolution equations with mixed monotone nonlocal condition, Z. Angew. Math. Phys., 2014, 65(4), 711–728
  • [11] Jeet K., Bahuguna D., Monotone iterative technique for nonlocal fractional differential equations with finite delay in a Banach space, Electron. J. Qual. Theory Differ. Equ., 2015, 9, 1–16
  • [12] Chaudhary R., Pandey D. N., Monotone iterative technique for neutral fractional differential equation with infinite delay, Math. Methods Appl. Sci., 2016, 39(15), 4642–4653
  • [13] Chen P., Zhang X., Li Y., Iterative method for a new class of evolution equations with non-instantaneous impulses, Taiwanese J. Math., 2017, 21(4), 913–942
  • [14] Yan Z., On solutions of semilinear evolution integro-differential equations with nonlocal conditions, Tamkang J. Math., 2009,40(3), 257–269
  • [15] Haloi R., Pandey D. N., Bahuguna, D., Bahuguna, D., Existence uniqueness and asymptotic stability of solutions to nonautonomous semi-linear differential equations with deviated arguments, Nonlinear Dyn. Syst. Theory, 2012, 12(2), 179–191
  • [16] Chadha A., Pandey D. N., Mild solutions for non-autonomous impulsive semi-linear differential equations with iterated deviating arguments, Electron. J. Differ. Equ., 22015, 2015(222), 1–14
  • [17] El-Borai M. M., The fundamental solutions for fractional evolution equations of parabolic type, Bol. Asoc. Mat. Venez., 2004, XI(1), 29–43
  • [18] Li F., Existence for non-autonomous fractional integro-differential equations with nonlocal conditions, Abstr. Appl. Anal., 2013, Article ID 723453, DOI: 10.1155/2013/723453
  • [19] Chen P., Zhang X., Li Y., Study on fractional non-autonomous evolution equations with delay, Comput. Math. Appl., 2017, 73(5), 794–803
  • [20] Benchohra M., Neito J. J., Rezoug N., Second order evolution equations with nonlocal conditions, Demonstr. Math., 2017, 50, 309–319
  • [21] Chen P., Zhang X., Li Y., Fractional non-autonomous evolution equation with nonlocal conditions, J. Pseudo-Differ. Oper. Appl., DOI: 10.1007/s11868-018-0257-9
  • [22] Chen P., Zhang X., Li Y., A blowup alternative result for fractional non-autonomous evolution equation of Volterra type, Commun. Pure Appl. Anal., 2018, 17(5), 1975–1992
  • [23] Pazy A., Semigroup of Linear Operators and Applications to Partial Differential Equations, Applied Mathematical Sciences, Vol. 44, Springer-Verlag, New York, 1983
  • [24] Friedman A., Partial Differential Equations, Dover Publication, New York, 1997
  • [25] Heinz H. P., On the behaviour of noncompactness with respect to differentiation and integration of vector valued functions, Nonlinear Anal., 1983, 7(12), 1351–1371
  • [26] Deimling K., Nonlinear Functional Analysis, Springer-Verlag, Berlin, 1985
Uwagi
PL
Opracowanie rekordu w ramach umowy 509/P-DUN/2018 ze środków MNiSW przeznaczonych na działalność upowszechniającą naukę (2019).
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-f9cbe6aa-958e-4c0a-88d4-efc7e040f594
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