The boundary value problem for one class of higher-order nonlinear partial differential equations-Reference-Cited by-同舟云学术

The boundary value problem for one class of higher-order nonlinear partial differential equations

Published:2022-03-01 Issue:3 Volume:29 Page:387-395
ISSN:1072-947X
Container-title:Georgian Mathematical Journal
language:en
Short-container-title:

Author:

Kharibegashvili Sergo¹,Midodashvili Bidzina²

Affiliation:

1. A. Razmadze Mathematical Institute of I. Javakhishvili Tbilisi State University , 6 Tamarashvili Str., 0186; and Department of Mathematics, Georgian Technical University, 77 M. Kostava Str. , Tbilisi 0175 , Georgia

2. Faculty of Exact and Natural Sciences , I. Javakhishvili Tbilisi State University , 13 University Str. , Tbilisi 0186; and Faculty of Education, Exact and Natural Sciences, Gori State Teaching University, 5 I. Chavchavadze Str., Gori , Georgia

Abstract

Abstract In this paper, we consider the boundary value problem for one class of higher-order nonlinear partial differential equations. We prove theorems on existence, uniqueness and nonexistence of solutions of this problem.

Publisher

Walter de Gruyter GmbH

Subject

General Mathematics

Link

https://www.degruyter.com/document/doi/10.1515/gmj-2021-2139/pdf

Reference19 articles.

1. A. B. Aliev and B. H. Lichaei, Existence and non-existence of global solutions of the Cauchy problem for higher order semilinear pseudo-hyperbolic equations, Nonlinear Anal. 72 (2010), no. 7–8, 3275–3288.

2. X. Chen, Existence and nonexistence of global solutions for nonlinear evolution equation of fourth order, Appl. Math. J. Chinese Univ. Ser. B 16 (2001), no. 3, 251–258.

3. L. C. Evans, Partial Differential Equations, Grad. Stud. Math. 19, American Mathematical Society, Providence, 1998.

4. S. Fučík and A. Kufner, Nonlinear Differential Equations, Stud. Appl. Math. 2, Elsevier Scientific, Amsterdam, 1980.

5. V. A. Galaktionov, E. L. Mitidieri and S. I. Pohozaev, Blow-up for Higher-Order Parabolic, Hyperbolic, Dispersion and Schrödinger Equations, Monogr. Res. Notes Math., CRC Press, Boca Raton, 2015.

Cited by 1 articles. 订阅此论文施引文献订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献

1. Existence and uniqueness of solution for the nonlinear Brusselator system with Robin boundary conditions;Georgian Mathematical Journal;2023-11-20