By constructing a suitable projection scheme and using the coincidence degree theory of Mawhin, we study the existence of solutions for conjugate boundary value problems with functional boundary conditions at resonance with dim Ker L = 1. Examples are given to illustrate our main results.
In this paper, by using the coincidence degree theory due to Mawhin and constructing suitable operators, we study the solvability for functional boundary value problems of second-order nonlinear differential equations system at resonance with dim Ker L = 3 and 4, respectively.
By defining the Banach spaces endowed with the appropriate norm, constructing a suitable projection scheme, and using the coincidence degree theory due to Mawhin, we study the existence of solutions for functional boundary value problems at resonance on the half-line with $\operatorname{dim}\operatorname{Ker}L = 1$
dim
Ker
L
=
1
. And an example is given to show that our result here is valid.
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