Abstract
In this paper, using topological degree and linear algebra techniques, we prove that a certain class of quasi-linear systems of differential equations of the form x ˙ = Ax + μ f ( x , μ ) has at least one periodic solution, where μ is a small parameter and A is a constant n × n matrix. If μ is bounded away from zero and the components of f are polynomials in x 1 , … , x n , μ , then there exists at least one periodic solution under certain conditions. Finally, we consider several examples.
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