Abstract
Under a resonance condition involving integral boundary value problems for a second-order nonlinear differential equation in mathbb{R}^{n}, we show its solvability by using the coincidence degree theory of Mawhin and the theory of matrix diagonalization in linear algebra.
Highlights
Let A =n×n be a square matrix of order n. α : [0, 1] → R is a bounded variation function, and
There have been many papers addressing the existence of solutions for differential systems of coupled integral boundary value problems; see, for example, [1, 3, 5–7, 9, 11–14]
We define L to be the linear operator from D(L) ⊂ X to Y with dom L = u ∈ X0 : u(0) = 0, u(1) = A u(t) dα(t) and for u ∈ D(L), Lu = –u
Summary
We will study the existence of solutions for the following integral boundary value problem at resonance in Rn: There have been many papers addressing the existence of solutions for differential systems of coupled integral boundary value problems; see, for example, [1, 3, 5–7, 9, 11–14]. Theorem 1.1 ([19] (Mawhin continuation theorem)) Let L : dom L ⊂ X → Y be a Fredholm operator of index zero and N be L-compact on Ω.
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