Abstract
We present a survey on the existence of nontrivial solutions to impulsive differential equations by using variational methods, including solutions to boundary value problems, periodic solutions, and homoclinic solutions.
Highlights
There are many processes and phenomena in the real world, which are subjected during their development to the shortterm external influences
We present a survey on the existence of nontrivial solutions to impulsive differential equations by using variational methods, including solutions to boundary value problems, periodic solutions, and homoclinic solutions
It can be assumed that these external effects are “instantaneous”; that is, they are in the form of impulses. The investigation of such “leaps and bounds” developing dynamical states is a subject of different sciences: mechanics, control theory, pharmacokinetics, epidemiology, population dynamics, economics, ecology, and so forth
Summary
There are many processes and phenomena in the real world, which are subjected during their development to the shortterm external influences. Variational methods have been widely used to study impulsive problems, such as boundary value problems, periodic solutions, and homoclinic solutions. We will explore the variational framework of impulsive differential equations and study the existence and multiplicity of solutions of boundary value problems, periodic solutions, and homoclinic solutions. We must note that besides the results presented in this survey many interesting and important results on impulsive differential equations via variational methods have been obtained by other researchers; see, for example, [23,24,25,26,27,28,29,30,31] and the references cited therein
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