[PDF] Top 20 Variational approach to a class of impulsive differential equations

... By using the Mountain Pass Lemma and the Minimax Principle established by Am- brosetti and Rabinowitz [, ], we have obtained in [] the existence of a nontrivial solution and the existence of infinitely many ... See full document

... of variational construction for prob- lem () in an appropriate space of functions in this ...differential equations case and the difference equations ... See full document

... The paper is organized as follows. In Section , we obtain the existence, uniqueness, and asymptotical stability of the exact solutions of (.). In Section , we study the asymptotical stability of the Runge-Kutta ... See full document

... In [] Luo et al. and [] Guo et al. gave some excellent results on the oscillation and nonoscillation of Eq. (.) by using associated Riccati techniques and an equivalence trans- formation. Moreover, Luo et al. ... See full document

... involving impulsive act, for retarded and neu- tral functional differential equations we cite [7-17], for applications of impulsive differ- ential equations on biology and neural ... See full document

... used variational methods to study the existence of solutions for boundary value problems 10–16, especially, in 14–16, the authors have studied the existence of infinitely many solutions by using variational ... See full document

... erential equations have been in- vestigated by several authors, (see, ...a class of first-order semilinear functional differential equations for which the nonlocal conditions and the impulse effects ... See full document

... a class of multi-term time-fractional impulsive integro-differential equations with state dependent delay subject to some fractional order integral boundary ... See full document

... Differential equations with impulsive effect provide mathematical models for many phenomena and processes in the field of natural sciences and ...functional differential systems has come into ... See full document

... for impulsive Sturm-Liouville differential equations (see [26],[23], [24], [25], [16], [21], ...Sturm-Liouville impulsive problem via critical point theory, variational methods and ... See full document

... new impulsive action, which starts at an arbitrary fixed point and keeps active on a finite time ...new class of abstract semilinear impulsive differential equations with non-instantaneous ... See full document

... the impulsive differential equation has been at- tracting the attention of several ...the variational method and some specific critical point theorems, such as mountain pass lemma, fountain theorem, linking ... See full document

... the impulsive boundary value problems for nonlinear fractional dif- ferential equations have not been addressed so extensively and many aspects of these prob- lems are yet to be ... See full document

... it has been studied extensively under various conditions. Here we mention some results. Byszewski and Lakshmikantham [], Byszewski [] obtained the existence and unique- ness of mild solutions and classical solutions ... See full document

... The impulsive differential equations constitute an important class of differential equa- ...These equations arise as a result of modeling the processes subject to abrupt (sud- den) changes and ... See full document

... a class of nonlinear impulsive fractional differential systems including Lipschitz continuous nonlinear ...applying variational methods, they obtained some new criteria guaran- teeing that the studied ... See full document

... a class of tenth-order boundary-value problems is ...the variational iteration method. Consider the following class of tenth-order boundary value ... See full document

... differential equations is gaining much importance and attention be- cause of its extensive applications in many engineering and scientific disciplines such as physics, chemistry, aerodynamics, electrodynamics of ... See full document

... By successful applications of nonlinear analysis and classical fixed point theory, we have developed adequate conditions under which the proposed class of implicit impulsive FODEs has at least one solution. ... See full document

... of impulsive dynamic equations provides a natural framework for mathematical modeling of many real world ...The impulsive ef- fects exist widely in many evolution processes in which their states are ... See full document