Ye, Yiwei2021-11-052021-11-052019-03-22Ye, 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. 1-17.1072-6691https://hdl.handle.net/10877/14776In 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.Text17 pages1 file (.pdf)enAttribution 4.0 InternationalFast homoclinic solutionsDamped vibration problemSubquadraticAsymptotically quadraticArticle