Abstract
Resonance and nonresonance periodic value problems of first-order differential systems are studied. Several new existence and uniqueness of solutions for the above problems are obtained. To establish such results sufficient conditions of limit forms are given. A necessary and sufficient condition for existence of nontrivial solution is also proved.
Highlights
This paper is concerned with the existence and uniqueness of solutions of the nonresonance periodic boundary value problems BVP for the first-order differential system: xtbtxtFt, x t, t ∈ 0, 1, 1.1
The paper is concerned with the existence and uniqueness of the resonance periodic boundary value problem of first-order: x t f t, x t, t ∈ 0, 1, 1.10
By a solution of BVPs 1.1 - 1.2 we mean that a function x ∈ C1 0, 1, Rn satisfies 1.1 - 1.2
Summary
This paper is concerned with the existence and uniqueness of solutions of the nonresonance periodic boundary value problems BVP for the first-order differential system: xtbtxtFt, x t , t ∈ 0, 1 , x0 x1, 1.2 where. The paper is concerned with the existence and uniqueness of the resonance periodic boundary value problem of first-order:. By a solution of BVPs 1.1 - 1.2 we mean that a function x ∈ C1 0, 1 , Rn satisfies 1.1 - 1.2. We are not sure that the above Theorem 1.2 and the other results in 1 are correct. The purpose of this paper is to establish several new existence and unique theorem for BVP 1.1 - 1.2. A new priori estimation on possible solutions of a family of BVP 1.1 - 1.2 is obtained and some ideas are from 1. For recent development on BVP 1.1 1.2 , except 1 , we are referred to the papers 2–9 and references cited therein
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