Time-antiperiodic and space-periodic boundary value problem for one class of semilinear partial differential equations-Reference-Cited by-同舟云学术

Time-antiperiodic and space-periodic boundary value problem for one class of semilinear partial differential equations

Published:2024-08-03 Issue: Volume: Page:
ISSN:1072-947X
Container-title:Georgian Mathematical Journal
language:en
Short-container-title:

Author:

Kharibegashvili Sergo¹,Midodashvili Bidzina²

Affiliation:

1. Department of Mathematics , Georgian Technical University , 77 M. Kostava Str. , Tbilisi 0175 ; and A. Razmadze Mathematical Institute of I. Javakhishvili Tbilisi State University, 2 Merab Aleksidze II lane, Tbilisi 0193 , 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 Teaching University, 5 I. Chavchavadze Str., Gori 1400 , Georgia

Abstract

Abstract In this work, a time-antiperiodic and space-periodic boundary value problem for one class of semilinear partial differential equations is studied. The theorems on existence, uniqueness and nonexistence of solutions of this problem are proved.

Publisher

Walter de Gruyter GmbH

Link

https://www.degruyter.com/document/doi/10.1515/gmj-2024-2046/pdf

Reference20 articles.

1. J. Angulo Pava, Nonlinear Dispersive Equations: Existence and Stability of Solitary and Periodic Travelling Wave Solutions, Math. Surveys Monogr. 156, American Mathematical Society, Providence, 2009.

2. S. Boussandel, Existence of solutions for nonlinear nonmonotone evolution equations in Banach spaces with anti-periodic boundary conditions, Appl. Math. 63 (2018), no. 5, 523–539.

3. H. Brézis, Periodic solutions of nonlinear vibrating strings and duality principles, Bull. Amer. Math. Soc. (N.S.) 8 (1983), no. 3, 409–426.

4. W. Dimbour and V. Valmorin, Asymptotically antiperiodic solutions for a nonlinear differential equations with piecewise constant argument in a Banach space, Appl. Math. 7 (2016), no. 15, 1726–1733.

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