Fast homoclinic solutions for damped vibration systems with subquadratic and asymptotically quadratic potentials
Texas State University, Department of Mathematics
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.
Fast homoclinic solutions, Damped vibration problem, Subquadratic, Asymptotically quadratic
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.