Infinitely many fast homoclinic solutions for different classes of damped vibration systems

IF 1.1 Q1 MATHEMATICS

Journal of Nonlinear Functional Analysis Pub Date : 2020-01-01 DOI:10.23952/jnfa.2020.46

M. Timoumi

引用次数: 0

Abstract

. In this paper, we study the existence and multiplicity of fast homoclinic orbits for the class of damped vibration systems ¨ where L ( t ) is not required to be either uniformly positive deﬁnite or coercive, and W ( t , x ) is of subquadratic or superquadratic growth as | x | → ∞ , or satisﬁes only local conditions near the origin (i.e., it can be subquadratic, superquadratic or asymptotically quadratic at inﬁnity). To the best of our knowl-edge, there is no result concerning the existence and multiplicity of homoclinic orbits for the system with the conditions.

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不同类型阻尼振动系统的无穷多快速同斜解

．本文研究了一类阻尼振动系统的快速同斜轨道的存在性和多重性，其中L (t)不要求一致正定或强制，W (t, x)在| x |→∞时是次二次或超二次增长，或仅满足原点附近的局部条件(即在无穷远处可以是次二次、超二次或渐近二次)。据我们所知，对于具有这些条件的系统，没有关于同斜轨道存在性和多重性的结果。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Journal of Nonlinear Functional Analysis Multiple-

CiteScore

2.40

自引率

0.00%

发文量

期刊介绍： Journal of Nonlinear Functional Analysis focuses on important developments in nonlinear functional analysis and its applications with a particular emphasis on topics include, but are not limited to: Approximation theory; Asymptotic behavior; Banach space geometric constant and its applications; Complementarity problems; Control theory; Dynamic systems; Fixed point theory and methods of computing fixed points; Fluid dynamics; Functional differential equations; Iteration theory, iterative and composite equations; Mathematical biology and ecology; Miscellaneous applications of nonlinear analysis; Multilinear algebra and tensor computation; Nonlinear eigenvalue problems and nonlinear spectral theory; Nonsmooth analysis, variational analysis, convex analysis and their applications; Numerical analysis; Optimal control; Optimization theory; Ordinary differential equations; Partial differential equations; Positive operator inequality and its applications in operator equation spectrum theory and so forth; Semidefinite programming polynomial optimization; Variational and other types of inequalities involving nonlinear mappings; Variational inequalities.