一类超二次阻尼振动系统的无穷多快速同斜轨道

IF 1.1 Q1 MATHEMATICS

Journal of Nonlinear Functional Analysis Pub Date : 2020-01-01 DOI:10.23952/jnfa.2020.8

M. Timoumi

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引用次数: 1

摘要

．在本文中,我们考虑下面的阻尼振动系统¨u (t) + q (t)˙u (t)−L (t) u (t) +∇W (t, u (t)) = 0,∀t∈R, q∈C (R, R), L∈C (R, R N 2)是一个对称矩阵值函数和W C (t) x)∈1 (R×R N, R)。我们证明存在无穷多快类解决方案系统时问(t) = (cid: 82) t 0 Q (s) ds→+∞| | t→∞,L是强制性和均匀正定和W (t, x)超是在第二个变量但无穷满足超有名的生长条件不像范Ambrosetti-Rabinowitz或的条件。

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Infinitely many fast homoclinic orbits for a class of superquadratic damped vibration systems

. In this paper, we consider the following damped vibration system ¨ u ( t )+ q ( t ) ˙ u ( t ) − L ( t ) u ( t )+ ∇ W ( t , u ( t )) = 0 , ∀ t ∈ R , where q ∈ C ( R , R ) , L ∈ C ( R , R N 2 ) is a symmetric matrix valued function and W ( t , x ) ∈ C 1 ( R × R N , R ) . We prove the existence of inﬁnitely many fast homoclinic solutions for the system when Q ( t ) = (cid:82) t 0 q ( s ) ds → + ∞ as | t | → ∞ , L is neither coercive nor uniformly positive deﬁnite and W ( t , x ) is superquadratic at inﬁnity in the second variable but does not satisfy the well-known superquadratic growth conditions like the Ambrosetti-Rabinowitz or the Fei’s conditions.

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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.