AbstractIn this article we study the existence of positive solutions for second-order nonlinear neutral dynamic equations on time scales. The main tool employed here is Schauder’s fixed point theorem. The results obtained here extend the work of Culakova, Hanustiakova and Olach [12]. Two examples are also given to illustrate this work.
In this paper, four functionals fixed point theorem is used to investigate
the existence of positive solutions for second-order time-scale boundary
value problem of impulsive dynamic equations on the half-line.
We investigate the existence and iteration of positive solutions for the following third-orderp-Laplacian dynamic equations on time scales:(ϕp(uΔΔ(t)))∇+q(t)f(t,u(t),uΔΔ(t))=0, t∈[a,b],αu(ρ(a))-βuΔ(ρ(a))=0, γu(b)+δuΔ(b)=0, uΔΔ(ρ(a))=0,whereϕp(s)isp-Laplacian operator; that is,ϕp(s)=sp-2s, p>1, ϕp-1=ϕq, and1/p+1/q=1.By applying the monotone iterative technique and without the assumption of the existence of lower and upper solutions, we not only obtain the existence of positive solutions for the problem, but also establish iterative schemes for approximating the solutions.
We study the existence of positive solutions to the system of nonlinear first-order periodic boundary value problems on time scalesxΔ(t)+P(t)x(σ(t))=F(t,x(σ(t))),t∈[0,T]T,x(0)=x(σ(T)), by using a well-known fixed point theorem in cones. Moreover, we characterize the eigenvalue intervals forxΔ(t)+P(t)x(σ(t))=λH(t)G(x(σ(t))),t∈[0,T]T,x(0)=x(σ(T)).
AbstractIn this paper, some criteria for the existence of positive solutions of a class of systems of impulsive dynamic equations on time scales are obtained by using a fixed point theorem in cones.
We consider the existence of positive solutions of nonlinearp-Laplaciandynamic equations with derivative on time scales. Applying the Avery-Peterson fixed point theorem, we obtain at least three positive solutions to the problem. An example is also presented to illustrate the applications of the obtained results.
Existence of positive solutions for second-order nonlinear neutral dynamic equations on time scales
