Two and three positive solutions of m-point boundary value problems for functional dynamic equations on time scales

Abstract

In this paper, by using fixed point theorems in a cone, we study the existence of at least two and three positive solutions of a nonlinear second-order m-point boundary value problem for functional dynamic equations on time scales. As an application, we also give an example to demonstrate our results.

Existence of positive solutions for multi-point time scale boundary value problems on infinite intervals

“…Much of theory of time scale dynamic equations on finite intervals have been presented in [5,7,13,14,15,16,17,20,21,18,19,22,23] and references therein. However, there is significantly less literature available on the basic theory of time scale dynamic equations on infinite intervals.…”

Existence and Uniqueness of Positive Solutions for Second-Order Sturm-Liouville and Multi-Point Problems on Time Scales

“…Our method was based on the associated Green's function obtained in [13]. In essence, we combined the method of lower and upper solutions with the cone expansion and compression fixed point theorem of norm type.…”

Positive solutions to the singular p-Laplacian BVPs with sign-changing nonlinearities and higher-order derivatives in Banach spaces on time scales

“…It is notable that results on time scales in [6][7][8][9][10][11][12][13] are mainly concerned with the existence of positive solutions to the BVPs with the nonlinear terms which do not involve the higher-order derivatives explicitly and the nonlinear function f has continuity (rd-continuity), so that the corresponding solution operator has continuity (rd-continuity). It is obvious that weakening the existence conditions of the BVPs has been an interesting subject in differential equations and related dynamical systems, especially when the function f (t, x, y) or f (t, x) is only continuous with respect to t in Banach spaces.…”

“…Nowadays the theory on time scales has been widely applied to several scientific fields such as biology, heat transfer, stock market, wound healing and epidemic models [2][3][4][5] etc. Recently, considerable works have been undertaken in the existence problems of solutions to dynamic systems on time scales, for details, see [6][7][8][9][10][11][12][13] and the references therein.…”