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Existence of classical solutions for initial boundary value problems for nonlinear dispersive equations of odd-orders


Abstract

In this paper we investigate a class of initial boundary value problems for a class of nonlinear dispersive equations of odd orders. We prove existence of at least one solution and existence of at least one nonnegative solution. Our method is based on a use of a fixed point theory for the sum of two operators.

У статті досліджено клас початкових граничних задач для класу нелінійних дисперсійних рівняння непарних порядків. Доведено існування принаймні одного розв’язоку і існування хоча б одного невід’ємного розв'язку. Наш метод базується на використанні теорії про нерухомі точки для суми двох операторів.

Key words: High-order dispersive equations, global solutions, initial boundary value problems, fixed point, Sum of operators.


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Article Information

TitleExistence of classical solutions for initial boundary value problems for nonlinear dispersive equations of odd-orders
SourceMethods Funct. Anal. Topology, Vol. 28 (2022), no. 3, 228-241
DOI10.31392/MFAT-npu26_3.2022.03
MathSciNet   MR4550660
Milestones  Received 30/03/2022; Revised 06/08/2022
CopyrightThe Author(s) 2022 (CC BY-SA)

Authors Information

Svetlin Georgiev Georgiev
Department of Differential Equations, Faculty of Mathematics and Informatics, University of Sofia, Sofia, Bulgaria

Arezki Kheloufi
Laboratory of Applied Mathematics, Bejaia University, 06000 Bejaia, Algeria

Karima Mebarki
Laboratory of Applied Mathematics, Faculty of Exact Sciences, Bejaia University, 06000 Bejaia, Algeria


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Citation Example

Svetlin Georgiev Georgiev, Arezki Kheloufi, and Karima Mebarki, Existence of classical solutions for initial boundary value problems for nonlinear dispersive equations of odd-orders, Methods Funct. Anal. Topology 28 (2022), no. 3, 228-241.


BibTex

@article {MFAT1796,
    AUTHOR = {Svetlin Georgiev Georgiev and Arezki Kheloufi and Karima Mebarki},
     TITLE = {Existence of classical solutions for initial boundary value problems for nonlinear dispersive equations of odd-orders},
   JOURNAL = {Methods Funct. Anal. Topology},
  FJOURNAL = {Methods of Functional Analysis and Topology},
    VOLUME = {28},
      YEAR = {2022},
    NUMBER = {3},
     PAGES = {228-241},
      ISSN = {1029-3531},
  MRNUMBER = {MR4550660},
       DOI = {10.31392/MFAT-npu26_3.2022.03},
       URL = {http://mfat.imath.kiev.ua/article/?id=1796},
}


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