In this article, we study the nonperiodic damped vibration problem
where L(t) is uniformly positive definite for all , and W(t,x) is either subquadratic or asymptotically quadratic in x as . Based on the minimax method in critical point theory, we prove the existence and multiplicity of fast homoclinic solutions for the above problem.
Submitted November 3, 2017. Published March 22, 2019.
Math Subject Classifications: 34C37, 37J45.
Key Words: Fast homoclinic solutions; damped vibration problem; subquadratic; asymptotically quadratic.
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| Yiwei Ye |
School of Mathematical Science
Chongqing Normal University
Chongqing 401331, China
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