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Existence and multiplicity of fast homoclinic solutions for a class of damped vibration problems with impulsive effects. (English) Zbl 1474.34289

Summary: This paper is concerned with the existence and multiplicity of fast homoclinic solutions for a class of damped vibration problems with impulsive effects. Some new results are obtained under more relaxed conditions by using Mountain Pass Theorem and Symmetric Mountain Pass Theorem in critical point theory. The results obtained in this paper generalize and improve some existing works in the literature.

MSC:

34C37 Homoclinic and heteroclinic solutions to ordinary differential equations
34A37 Ordinary differential equations with impulses
34B37 Boundary value problems with impulses for ordinary differential equations
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