Infinitely Many Periodic Solutions for a Class of Perturbed Second-Order Differential Equations with Impulses

Heidarkhani, Shapour; Феррара, Массимилиано; Salari, Amjad

doi:10.1007/s10440-014-9970-4

Cited by 27 publications

(10 citation statements)

References 35 publications

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“…In the context of reducing the number of hours taught in the classroom, if students do not take the initiative to practice English and practice outside the classroom, it is impossible to master and apply the knowledge acquired in a limited time, and their academic performance will be difficult to improve. According to the characteristics of language learning, students can closely link classroom learning with daily practice to learn English [2]. Translation is a very practical subject.…”

Section: Introductionmentioning

confidence: 99%

Construction of the Teaching Model of Second Classroom of Translation Based on Network Platform

Liu¹

2019

JSS

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In order to further deepen the reform of college English teaching and improve the translation level of students, a teaching model of second classroom of translation based on network platform was proposed. The second classroom activities include audio visual group activities, conversational group activities, reading group activities, writing group activities, teaching group activities, research innovation and translation team activities. The organization and evaluation of the second classroom activities include the second classroom annual work plan, student scope, teacher and student assessment, and work summary. The results show that the second classroom fully mobilizes the initiative and enthusiasm of students to learn language and create a good learning environment. The translation level of students is improved, and they become applied talents. Therefore, the second classroom teaching mode can improve students' enthusiasm for college English courses, promote the exchange of classroom teaching, and improve the teaching effect of college English courses. In addition, students achieve better results in the second classroom mode than in the traditional mode. At the same time, the second classroom teaching mode helps students to improve their self-learning ability and effectively promote personalized learning.

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Section: Introductionmentioning

confidence: 99%

Construction of the Teaching Model of Second Classroom of Translation Based on Network Platform

Liu¹

2019

JSS

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“…For the background and applications of the theory of impulsive differential equations to different areas, we refer the reader to the classical monograph [17]. For the general aspects of impulsive differential equations, we refer the reader to [18,19,20]. The existence of multiple solutions of impulsive problems has been studied also using the variational methods and critical point theory (see [21]).…”

Section: Introductionmentioning

confidence: 99%

Energy estimate for impulsive fractional advection dispersion equations in anomalous diffusions

2018

J. Nonlinear Funct. Anal.

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This paper deals with the existence and energy estimates of solutions for a class of impulsive fractional advection dispersion equations in anomalous diffusions, while the nonlinear part of the problem admits some hypotheses on the behavior at origin or perturbation property. In particular, for a precise localization of the parameter, the existence of a non-zero solution is established requiring the sublinearity of nonlinear part at origin and infinity. We also consider the existence of solutions for our problem under algebraic conditions with the classical Ambrosetti-Rabinowitz. By combining two algebraic conditions on the nonlinear term which guarantees the existence of two solutions as well as applying the mountain pass theorem given by Pucci and Serrin, we establish the existence of the third solution for our problem. Moreover, concrete examples of applications are also provided.

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“…There are some common techniques to approach these problems: Fixed point theorems [8,9,31], the method of upper and lower solutions [7], and topological degree theory [37]. In the last few years, variational methods and critical point theory have been used to determine the existence of solutions for impulsive differential equations under certain boundary conditions, see [1,21,43,44,46,48] and the references therein. We note that the difficulties dealing with such problems are that their states are discontinuous.…”

Section: Introductionmentioning

confidence: 99%

Existence of three solutions for impulsive multi-point boundary value problems

Böhner

Heidarkhani

Salari

et al. 2017

OpMath

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Infinitely Many Periodic Solutions for a Class of Perturbed Second-Order Differential Equations with Impulses

Cited by 27 publications

References 35 publications

Construction of the Teaching Model of Second Classroom of Translation Based on Network Platform

Construction of the Teaching Model of Second Classroom of Translation Based on Network Platform

Energy estimate for impulsive fractional advection dispersion equations in anomalous diffusions

Existence of three solutions for impulsive multi-point boundary value problems

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