Resonance Conditions For The Existence Of Periodic Solution Of The System When

In this paper, we study the existence of periodic solutions of the isochronoussystemunder resonant situation. Assume that all the solutions of x'' + V'(x) = 0 are (2Ï€)/n periodic andhold. In addition, the limits and exist andare bounded. We prove that iforis of constant, the Eq. (1) has at least one 2Ï€-periodic solution. Moreover, we also prove the existence of 2Ï€-periodic of Eq. (1) provided that g(x) is sublinear and F(x) is bounded.