Two-body strong decays of the <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mn>2</mml:mn><mml:mi>P</mml:mi></mml:math> and <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mn>3</mml:mn><mml:mi>P</mml:mi></mml:math> charmonium states

Two-body open charm strong decays of the $2P$ and $3P$ charmonium states are studied by Bethe-Salpeter(BS) method combined with $^3P_0$ model. The wave functions mass spectra obtained solving BS equation relativistic correction. decay widths relative ratios calculated. Comparing our results experimental data, we obtain some interesting results. Considering $X^*(3860)$ as $\chi_{c0}(2P)$, total width is smaller than data. But depends on parameter $\gamma$ in model, have large errors, cannot rule out possibility that $\chi_{c0}(2P)$. $X(4160)$ a good candidate for $\chi_{c0}(3P)$, not only $\chi_{c0}(3P)$ same but $\frac{\Gamma(\chi_{c0}(3P)\to D\bar D)}{\Gamma(\chi_{c0}(3P)\to D^*\bar D^*)}\approx0.0019<0.09$, $\frac{\Gamma({\chi_{c0}(3P)\to D^*})}{\Gamma({\chi_{c0}(3P)\to D^*})}=0<0.22$ consistent $X(4160)$. Taking $X(4274)$ $\chi_{c1}(3P)$, so $\chi_{c1}(3P)$. Assigning $X(4350)$ $\chi_{c2}(3P)$, corresponding slightly larger To identify if many more investigations needed. All can provide useful information to discover confirm these particles future.