Existence of Positive Solutions for Second-Order Impulsive Boundary Value Problems on Time Scales

Abstract

In this paper, by using Leray-Schauder fixed-point theorem, Avery-Henderson fixed-point theorem and Leggett-Williams fixed-point theorem, respectively, we investigate the conditions for the existence of at least one, two and three positive solutions to nonlinear second-order impulsive boundary value problems on time scales.Mathematics Subject Classification. Primary 34B18; Secondary 34B37, 34N05.

Existence of positive solutions for second order impulsive differential equations with integral boundary conditions on the real line

“…Then by (H5), (H7), (H8), (H9), the properties ( 6), (7) and the Lebegue dominated convergence theorem, we have…”

Impulsive Diffusion Equation on Time Scales

“…Yilmaz, Koyunbakan and Ic gave some substantial results for diffusion equation on T in 2015 [16]. Yaslan [17] proved the existence of positive solutions for second-order impulsive BVP's on T in 2016. Allahverdiev, Eryilmaz and Tuna [18] considered dissipative SL operators with a spectral parameter under the boundary condition on bounded time scales in 2017.…”

Positive Solutions for Second Order Impulsive Differential Equations with Integral Boundary Conditions on an Infinite Interval

“…The existence and multiplicity of positive solutions for linear and nonlinear second-order impulsive dynamic equations have been extensively studied, see [4,5,8,9,10]. Due to the fact that an infinite interval is noncompact, the discussion about boundary value problems on the half-line more complicated, in particular, for impulsive IBVP on an infinite interval, few works were done, see [19,23].…”