6,553 research outputs found
Existence of positive solutions for non local p-Laplacian thermistor problems on time scales
We make use of the Guo-Krasnoselskii fixed point theorem on cones to prove existence of positive solutions to a non local p-Laplacian boundary value problem on time scales arising in many applications. © 2007 Victoria University. All rights reserved.CEOCFCTFEDER/POCTISFRH/BPD/20934/200
Qualitative analysis of dynamic equations on time scales
In this article, we establish the Picard-Lindelof theorem and approximating
results for dynamic equations on time scale. We present a simple proof for the
existence and uniqueness of the solution. The proof is produced by using
convergence and Weierstrass M-test. Furthermore, we show that the Lispchitz
condition is not necessary for uniqueness. The existence of epsilon-approximate
solution is established under suitable assumptions. Moreover, we study the
approximate solution of the dynamic equation with delay by studying the
solution of the corresponding dynamic equation with piecewise constant
argument. We show that the exponential stability is preserved in such
approximations.Comment: 13 page
Global stability of steady states in the classical Stefan problem
The classical one-phase Stefan problem (without surface tension) allows for a
continuum of steady state solutions, given by an arbitrary (but sufficiently
smooth) domain together with zero temperature. We prove global-in-time
stability of such steady states, assuming a sufficient degree of smoothness on
the initial domain, but without any a priori restriction on the convexity
properties of the initial shape. This is an extension of our previous result
[28] in which we studied nearly spherical shapes.Comment: 14 pages. arXiv admin note: substantial text overlap with
arXiv:1212.142
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
On fast-slow consensus networks with a dynamic weight
We study dynamic networks under an undirected consensus communication
protocol and with one state-dependent weighted edge. We assume that the
aforementioned dynamic edge can take values over the whole real numbers, and
that its behaviour depends on the nodes it connects and on an extrinsic slow
variable. We show that, under mild conditions on the weight, there exists a
reduction such that the dynamics of the network are organized by a
transcritical singularity. As such, we detail a slow passage through a
transcritical singularity for a simple network, and we observe that an exchange
between consensus and clustering of the nodes is possible. In contrast to the
classical planar fast-slow transcritical singularity, the network structure of
the system under consideration induces the presence of a maximal canard. Our
main tool of analysis is the blow-up method. Thus, we also focus on tracking
the effects of the blow-up transformation on the network's structure. We show
that on each blow-up chart one recovers a particular dynamic network related to
the original one. We further indicate a numerical issue produced by the slow
passage through the transcritical singularity
Multiple positive solutions for functional dynamic equations on time scales
AbstractIn this paper, we study the following functional dynamic equation on time scales: {[Φ(uΔ(t))]∇+a(t)f(u(t),u(μ(t)))=0,t∈(0,T)T,u(t)=φ(t),t∈[−r,0)T,u(0)−B0(uΔ(0))=0,uΔ(T)=0, where Φ:R→R is an increasing homeomorphism and a positive homomorphism and Φ(0)=0. By using the well-known Leggett–Williams fixed point theorem, existence criteria for multiple positive solutions are established. An example is also given to illustrate the main results
Existence of three positive solutions to some p-Laplacian boundary value problems
We obtain, by using the Leggett-Williams fixed point theorem, sufficient conditions that ensure the existence of at least three positive solutions to some p-Laplacian boundary value problems on time scales. © 2013 Moulay Rchid Sidi Ammi and Delfim F. M. Torres
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