Abstract
In this paper, the author discusses the multiple positive solutions for an infinite three-point boundary value problem of first-order impulsive superlinear singular integro-differential equations on the half line in a Banach space by means of the fixed-point theorem of cone expansion and compression with norm type. MSC: 45J05; 34G20; 47H10
Highlights
In recent years, multiple solutions of boundary value problems for impulsive differential equations in scalar spaces had been extensively studied
By constructing a bounded closed convex set, apart from the singularities, and using the Schauder fixed-point theorem, he obtained the existence of positive solutions for the infinite boundary value problems
In this paper, we shall discuss the existence of two positive solutions for first-order superlinear singular equations by means of a different method, i.e., by using the fixed-point theorem of cone expansion and compression with norm type, and the key point is to introduce a new cone Q
Summary
Multiple solutions of boundary value problems for impulsive differential equations in scalar spaces had been extensively studied (see, for example, [ – ]). Guo discussed two infinite boundary value problems for nth-order impulsive nonlinear singular integro-differential equations of mixed type on the half line in a Banach space. By constructing a bounded closed convex set, apart from the singularities, and using the Schauder fixed-point theorem, he obtained the existence of positive solutions for the infinite boundary value problems. Such equations are sublinear, and there are no results on existence of two positive solutions. Consider the infinite three-point boundary value problem for a first-order impulsive nonlinear singular integro-differential equation of mixed type on the half line in E:.
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