We consider the stability of ground state solitary waves of the generalized Ostrovsky equation \documentclass[12pt]{minimal}
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\begin{document}$$( u_t - \beta u_{xxx} + f(u)_x)_x = \gamma u$$\end{document}, with homogeneous nonlinearities of the form \documentclass[12pt]{minimal}
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\begin{document}$$f(u)=a_e|u|^p+a_o|u|^{p-1}u$$\end{document}. We obtain bounds on the function \documentclass[12pt]{minimal}
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\begin{document}$$d$$\end{document} whose convexity determines the stability of the solitary waves. These bounds imply that, when \documentclass[12pt]{minimal}
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\begin{document}$$2\le p<5$$\end{document} and \documentclass[12pt]{minimal}
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\begin{document}$$a_o<0$$\end{document}, solitary waves are stable for \documentclass[12pt]{minimal}
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\begin{document}$$c$$\end{document} near \documentclass[12pt]{minimal}
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\begin{document}$$c_*=2\sqrt{\beta \gamma }$$\end{document}. These bounds also imply that, for \documentclass[12pt]{minimal}
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\begin{document}$$\gamma >0$$\end{document} small, solitary waves are stable when \documentclass[12pt]{minimal}
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\begin{document}$$2\le p<5$$\end{document} and unstable when \documentclass[12pt]{minimal}
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\begin{document}$$p>5$$\end{document}. We also numerically compute the function \documentclass[12pt]{minimal}
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\begin{document}$$d$$\end{document}, and thereby determine precise regions of stability and instability, for several nonlinearities.
