On the Solvability of One Boundary Value Problem for a Class of Higher-Order Nonlinear Partial Differential Equations

被引：0
作者：
S. Kharibegashvili
B. Midodashvili
机构：
[1] I. Javakhishvili Tbilisi State University,A. Razmadze Mathematical Institute
[2] Georgian Technical University,Department of Mathematics
[3] I. Javakhishvili Tbilisi State University,Faculty of Exact and Natural Sciences
[4] Gori State Teaching University,Faculty of Education, Exact and Natural Sciences
来源：
Mediterranean Journal of Mathematics | 2021年 / 18卷
关键词：
Nonlinear higher-order equations; Schaefer’s fixed point theorem; existence; uniqueness and nonexistence of solutions; Primary 35G30; Secondary 00A00;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
The boundary value problem for a class of higher-order nonlinear partial differential equations is considered. The theorems on existence, uniqueness and nonexistence of solutions of this problem are proved.
引用
收藏
相关论文
共 17 条
[1]  
Aliev AB(2010)Existence and nonexistence of global solutions of the Cauchy problem for higher order semilinear pseudohyperbolic equations J. Nonlinear Anal. Theory Methods Appl. 72 3275-3288
[2]  
Lichaei BH(2009)Boundary value problems for some classes of nonlinear wave equations Mem. Differ. Equ. Math. Phys. 46 1-114
[3]  
Kharibegashvili S(2008)Solvability of characteristic boundary-value problems for nonlinear equations with iterated wave operator in the principal part Electron. J. Differ. Equ. 2008 1-12
[4]  
Kharibegashvili S(2008)On one boundary value problem for a nonlinear equation with iterated wave operator in the principal part Ga. Math. J. 15 541-554
[5]  
Midodashvili B(2017)Raja Ben-Rabha: on strong well-posedness of initial-boundary value problems for higher order nonlinear hyperbolic equations with two independent variables Ga. Math. J. 24 409-428
[6]  
Kharibegashvili S(2017)On local existence and blow-up solutions for nonlinear wave equations of higher-order Kirchhoff type with strong dissipation IJMNTA 6 11-25
[7]  
Midodashvili B(2016)Asymptotic behaviour of solutions to a class of fourth-order nonlinear evolution equations with dispersive and dissipative terms J. Inequal. Appl. 318 1-7
[8]  
Kiguradze T(2010)Existence and nonexistence of global solutions for a class of nonlinear wave equations of higher order J. Nonlinear Anal. Theory Methods Appl. 72 4500-4507
[9]  
Lin G(2001)Existence and nonexistence of global solutions for nonlinear evolution equation of fourth order Appl. Math. J. Chin. Univ. Ser. B 16 251-258
[10]  
Gao Y(undefined)undefined undefined undefined undefined-undefined
12