Impulsive Periodic Solutions for Singular Problems via Variational Methods

Abstract

In this paper we study impulsive periodic solutions for second-order nonautonomous singular differential equations. Our proof is based on the mountain pass theorem. Some recent results in the literature are extended.2010 Mathematics subject classification: primary 34B15.

Solitary Wave and Periodic Wave Solutions for a Class of Singular p-Laplacian Systems with Impulsive Effeects

“…The existence periodic solutions and homoclinic solutions of different kinds of singular equations has been proposed by many authors, see [3], [5], [6], [7], [11], [13], [20], [27], [28], [33] and the references therein. Singular problems with impulsive effects have been scarcely studied, see [1], [12], [23], [24]. For example, in [12], the author and Luo considered the following first-order singular problems:…”

Positive periodic solutions to impulsive delay differentialequations

“…In fact, it seems that the work [20] is the first paper along this line. We must emphasize that singular boundary value problems without impulses have attracted the attention of many researchers [1,2,6,14].…”

“…Recently, variational methods and critical point theory have been successfully employed to investigate impulsive differential equations when the nonlinearity is regular; the existence and multiplicity of solutions for impulsive boundary value problems have been considered in [9,16,[19][20][21][22][23][24][25][26][27][28].…”

Existence for Singular Periodic Problems: A Survey of Recent Results

“…In the literature, two different approaches have been used to establish the existence results for singular equations. The first one is the variational approach [3,4,6,19,20] and the second one is topological methods [1,10,[21][22][23][24][25][26][27][28]. In our opinion, the first important result was proved in the pioneering paper of Lazer and Solimini [29].…”