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Supported by the use of a regular scalar field we find a black hole solutionin the Einstein-Gauss-Bonnet model. From the obtained solution we can recoverthe Schwarzschild black hole as in other works. Later, by implementing the oddparity perturbations method we study the stability of the linearized equationsof motion of the model, we find the explicit form of the Regge-Wheelerpotential and we explore the condition of vanishing perturbations at thehorizon of the black hole. We test the stability of the obtained solution bychecking the positivity condition of the Regge-Wheeler potential. Finally, weshow that the stability of model depends on the value of a parameter introducedin the profile for the scalar field.

Hairy black hole stability under odd parity perturbations in the Einstein-Gauss-Bonnet model