Existence of positive solutions to second-order time scale systems

Existence of positive solutions for a second-order p-Laplacian impulsive boundary value problem on time scales

In this paper, we investigate the existence of positive solutions for a second-order multipoint p-Laplacian impulsive boundary value problem on time scales. Using a new fixed point theorem in a cone, sufficient conditions for the existence of at least three positive solutions are established. An illustrative example is also presented.

Existence of Solutions to Second-Order BVPs on Time Scales

2 School of Mathematics The University of New South Wales, Sydney NSW 2052, Australia Abstract:We consider a boundary value problem (BVP) for systems of second-order dynamic equations on time scales. Using methods involving dynamic inequalities, we formulate conditions under which all solutions to a certain family of systems of dynamic equations satisfy certain a priori bounds. These results ar...

Existence of Positive Solutions of Second Order Neutral Dynamic Equations on Time Scales

In this paper, a class of second order neutral dynamic equations on time scales is studied. Various types of eventually positive solutions are given and the existence of these eventually positive solutions are then derived by means of Kranoselskii’s fixed point theorem. AMS subject classification: 34K25, 34K40.

Existence Criteria and Classification Schemes for Positive Solutions of Second-order Nonlinear Difference Systems

Classification schemes for positive solutions of a class of second-order nonlinear difference systems are given in terms of their asymptotic magnitudes; and necessary as well as sufficient conditions for the existence of these solutions are also provided. Finally, some examples are given to illustrate the main results.

Optimal Control of Second Order Systems with Infinite Time Horizon: Existence of Solutions