CLASSICAL SOLUTIONS FOR A CLASS OF NONLINEAR WAVE EQUATIONS

被引：1

作者：

Georgiev, Svetlin ^{[1
]}

Mebarki, Karima ^{[2
]}

Zennir, Khaled ^{[3
,4
]}

机构：

[1] Univ Sofia, Fac Math & Informat, Dept Differential Equat, Sofia, Bulgaria

[2] Univ Bejaia, Fac Exact Sci, Lab Appl Math, Bejaia, Algeria

[3] Qassim Univ, Coll Sci & Arts, Dept Math, Ar Rass, Saudi Arabia

[4] Univ 8 Mai 1945 Guelma, Lab Math Appl & Modelisat, Guelma, Algeria

来源：

THEORETICAL AND APPLIED MECHANICS | 2021年 / 48卷 / 02期

关键词：

hyperbolic equations; nonnegative solution; fixed point; cone; sum of operators; FIXED-POINT THEOREM; PERIODIC-SOLUTIONS; SUM;

D O I：

10.2298/TAM201123013G

中图分类号：

O3 [力学];

学科分类号：

08 ; 0801 ;

摘要：

We study a class of initial value problems subject to nonlinear partial differential equations of hyperbolic type. A new topological approach is applied to prove the existence of nontrivial nonnegative solutions. More precisely, we propose a new integral representation of the solutions for the considered initial value problems and using this integral representation we establish existence of classical solutions for the considered classes of nonlinear wave equations.

引用

页码：257 / 272

页数：16

共 18 条

[1] [Anonymous], 1999, LINEAR NONLINEAR WAV, DOI [DOI 10.1002/9781118032954, 10.1002/9781118032954]
[2] PERIODIC-SOLUTIONS OF NON-LINEAR VIBRATING STRINGS AND DUALITY PRINCIPLES
BREZIS, H
[J]. BULLETIN OF THE AMERICAN MATHEMATICAL SOCIETY, 1983, 8 (03) : 409 - 426
[3] BREZIS H, 1980, COMMUN PUR APPL MATH, V33, P665
[4] A fixed-point theorem of Krasnoselskii
Burton, TA
[J]. APPLIED MATHEMATICS LETTERS, 1998, 11 (01) : 85 - 88
[5] SOLUTIONS OF ASYMPTOTICALLY LINEAR OPERATOR-EQUATIONS VIA MORSE-THEORY
CHANG, KC
[J]. COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS, 1981, 34 (05) : 693 - 712
[6] MULTIPLE PERIODIC-SOLUTIONS FOR AN ASYMPTOTICALLY LINEAR WAVE-EQUATION
CHANG, KC
WU, SP
LI, SJ
[J]. INDIANA UNIVERSITY MATHEMATICS JOURNAL, 1982, 31 (05) : 721 - 731
[7] FIXED POINT INDEX THEORY FOR PERTURBATION OF EXPANSIVE MAPPINGS BY k-SET CONTRACTIONS
Djebali, Smail
Mebarki, Karima
[J]. TOPOLOGICAL METHODS IN NONLINEAR ANALYSIS, 2019, 54 (02) : 613 - 640
[8] Djebali S, 2018, J NONLINEAR CONVEX A, V19, P1029
[9] Georgiev S., 2020, Appl. Sci., V22, P66
[10] Georgiev S., 2020, Partial Differential Equations in Applied Mathematics, V2

← 1 2 →