Abstract
This paper uses a fixed point theorem in cones to investigate the multiple positive solutions of a boundary value problem for second-order impulsive singular differential equations on the half-line. The conditions for the existence of multiple positive solutions are established.
Highlights
The theory of singular impulsive differential equations has been emerging as an important area of investigation in recent years
In recent paper 3, by using the Krasnoselskii’s fixed point theorem, Kaufmann has discussed the existence of solutions for some second-order boundary value problem with impulsive effects on an unbounded domain
1, 2, . . . . We prove that T un → T u0
Summary
Consider the following nonlinear singular Sturm-Liouville boundary value problems for second-order impulsive differential equation on the half-line: ptutft, u 0, ∀t ∈ J , Δu tk Ik u tk , k 1, 2, . . . , n, αu 0 − β lim p t u t 0, 1.1 t→0 γu ∞ δ lim p t u t 0, t→ ∞. Consider the following nonlinear singular Sturm-Liouville boundary value problems for second-order impulsive differential equation on the half-line: ptutft, u 0, ∀t ∈ J , Δu tk Ik u tk , k 1, 2, . We point out that in a second-order differential equation u f t, u, u , one usually considers impulses in the position u and the velocity u. In recent paper 3 , by using the Krasnoselskii’s fixed point theorem, Kaufmann has discussed the existence of solutions for some second-order boundary value problem with impulsive effects on an unbounded domain. In Sun et al and Liu et al, respectively, discussed the existence and multiple positive solutions for singular SturmLiouville boundary value problems for second-order differential equation on the half-line.
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