Periodic solutions of the vibrating string equation with Neumann and Dirichlet boundary conditions and a discontinuous nonlinearity

被引：0

作者：

Pavlenko, V. N. ^{[1
,2
]}

Petrash, T. A. ^{[1
]}

机构：

[1] Chelyabinsk State Univ, Chelyabinsk, Russia

[2] Chelyabinsk State Univ, Physicomath Sci, Chelyabinsk, Russia

来源：

TRUDY INSTITUTA MATEMATIKI I MEKHANIKI URO RAN | 2012年 / 18卷 / 02期

关键词：

nonlinear equation of a vibrating string; discontinuous nonlinearity; generalized periodic solutions; resonance case;

D O I：

暂无

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We consider a mathematical model of a vibrating string under a force that is discontinuous with respect to the state variable. It is assumed that one end of the string is fixed while the other is free. If the kernel of the operator generated by the linear part of the equation with boundary conditions and periodicity condition is zero, then the nonlinearity grows sublinearly; otherwise, it is bounded. The existence of a 2 pi-periodic generalized solution is established by a topological method.

引用

页码：199 / 204

页数：6

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