214 research outputs found
Variational approach to second-order impulsive dynamic equations on time scales
The aim of this paper is to employ variational techniques and critical point
theory to prove some conditions for the existence of solutions to nonlinear
impulsive dynamic equation with homogeneous Dirichlet boundary conditions. Also
we will be interested in the solutions of the impulsive nonlinear problem with
linear derivative dependence satisfying an impulsive condition.Comment: 17 page
Multiplicity of solutions for Dirichlet boundary conditions of second-order quasilinear equations with impulsive effects
This paper deals with the multiplicity of solutions for Dirichlet boundary conditions of second-order quasilinear equations with impulsive effects. By using critical point theory, a new result is obtained. An example is given to illustrate the main result
Critical point approaches to second-order differential systems generated by impulses
Using variational methods and critical point theory, we establish multiplicity results of solutions for second-order differential systems generated by impulses. Indeed, employing two sorts of three critical points theorems, we establish the multiplicity results for weak solutions of the problem and verify that these solutions are generated by impulses.Publisher's Versio
An Application of Variant Fountain Theorems to a Class of Impulsive Differential Equations with Dirichlet Boundary Value Condition
We consider the existence of infinitely many classical solutions to a class of impulsive differential equations with Dirichlet boundary value condition. Our main tools are based on variant fountain theorems and variational method. We study the case in which the nonlinearity is sublinear. Some recent results are extended and improved
A sufficient and necessary condition of existence of blow-up radial solutions for a k-Hessian equation with a nonlinear operator
In this paper, we establish the results of nonexistence and existence of blow-up radial solutions for a k-Hessian equation with a nonlinear operator. Under some suitable growth conditions for nonlinearity, the result of nonexistence of blow-up solutions is established, a sufficient and necessary condition on existence of blow-up solutions is given, and some further results are obtained. 
Bound Sets Approach to Impulsive Floquet Problems for Vector Second-Order Differential Inclusions
In this paper, the existence and the localization of a solution of an impulsive vector multivalued second-order Floquet boundary value problem are investigated. The method used in the paper is based on the combination of a fixed point index technique with bound sets approach. At first, problems with upper-Carathéodory right-hand sides are investigated and it is shown afterwards how can the conditions be simplified in more regular case of upper semi-continuous right hand side. In this more regular case, the conditions ensuring the existence and the localization of a solution are put directly on the boundary of the considered bound set. This strict localization of the sufficient conditions is very significant since it allows some solutions to escape from the set of candidate solutions. In both cases, the C1-bounding functions with locally Lipschitzian gradients are considered at first and it is shown afterwards how the conditions change in case of C2-bounding functions. The paper concludes with an application of obtained results to Liénard-type equations and inclusions and the comparisons of our conclusions with the few results related to impulsive periodic and antiperiodic Liénard equations are obtained
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