Fast homoclinic solutions for damped vibration systems with subquadratic and asymptotically quadratic potentials
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Date
2019-03-22
Authors
Ye, Yiwei
Journal Title
Journal ISSN
Volume Title
Publisher
Texas State University, Department of Mathematics
Abstract
In this article, we study the nonperiodic damped vibration problem
ü(t) + q(t)u̇(t) - L(t)u(t) + ∇W(t, u(t)) = 0,
where L(t) is uniformly positive definite for all t ∈ ℝ, and W(t, x) is either subquadratic or asymptotically quadratic in x as |x| → ∞. Based on the minimax method in critical point theory, we prove the existence and multiplicity of fast homoclinic solutions for the above problem.
Description
Keywords
Fast homoclinic solutions, Damped vibration problem, Subquadratic, Asymptotically quadratic
Citation
Ye, Y. (2019). Fast homoclinic solutions for damped vibration systems with subquadratic and asymptotically quadratic potentials. <i>Electronic Journal of Differential Equations, 2019</i>(43), pp. 1-17.