Instability Effects in F(R)-Modified Gravity and in Gravitational Baryogenesis

The review is devoted to the development and subsequent application of methods for studying the stability of solutions of higher-order differential equations arising in various models of modified gravity and baryosynthesis. Major attention is paid to F(R)-modified theories proposed to describe the accelerated expansion of the universe and to baryon asymmetry generation in the framework of the spontaneous and gravitational baryogenesis.