具有非局部边界条件的时间尺度上的超线性阻尼振动问题

IF 2.6 3区数学 Q1 MATHEMATICS, APPLIED

Nonlinear Analysis-Modelling and Control Pub Date : 2022-07-19 DOI:10.15388/namc.2022.27.28343

Yongfang Wei, Zhanbing Bai

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引用次数: 0

摘要

利用变分法研究了一类时间尺度上具有非局部边界条件的超线性阻尼振动方程。我们考虑了Cerami条件，而非线性项不满足Ambrosetti–Rabinowitz条件，因此可以应用临界点理论。然后在适当的Sobolev空间中建立变分结构，得到无穷多个大能量解的存在性。最后，用两个例子证明了我们的结果。

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Superlinear damped vibration problems on time scales with nonlocal boundary conditions

This paper studies a class of superlinear damped vibration equations with nonlocal boundary conditions on time scales by using the calculus of variations. We consider the Cerami condition, while the nonlinear term does not satisfy Ambrosetti–Rabinowitz condition such that the critical point theory could be applied. Then we establish the variational structure in an appropriate Sobolev’s space, obtain the existence of infinitely many large energy solutions. Finally, two examples are given to prove our results.

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来源期刊

Nonlinear Analysis-Modelling and Control MATHEMATICS, APPLIED-MATHEMATICS, INTERDISCIPLINARY APPLICATIONS

CiteScore

3.80

自引率

10.00%

发文量

审稿时长

9.6 months

期刊介绍： The scope of the journal is to provide a multidisciplinary forum for scientists, researchers and engineers involved in research and design of nonlinear processes and phenomena, including the nonlinear modelling of phenomena of the nature. The journal accepts contributions on nonlinear phenomena and processes in any field of science and technology. The aims of the journal are: to provide a presentation of theoretical results and applications; to cover research results of multidisciplinary interest; to provide fast publishing of quality papers by extensive work of editors and referees; to provide an early access to the information by presenting the complete papers on Internet.