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The spin-1 Heisenberg model on a triangular lattice with the ferromagneticnearest, $J_1=-(1-p)J,$ $J>0$, and antiferromagnetic third-nearest-neighbor,$J_3=pJ$, exchange interactions is studied in the range of the parameter $0\leqslant p \leqslant 1$. Mori's projection operator technique is used as amethod, which retains the rotation symmetry of spin components and does notanticipate any magnetic ordering. For zero temperature several phasetransitions are observed. At $p\approx 0.2$ the ground state is transformedfrom the ferromagnetic spin structure into a disordered state, which in itsturn is changed to an antiferromagnetic long-range ordered state with theincommensurate ordering vector ${\bf Q = Q^\prime} \approx (1.16, 0)$ at$p\approx 0.31$. With the further growth of $p$ the ordering vector moves alongthe line ${\bf Q^\prime-Q_c}$ to the commensurate point ${\bfQ_c}=(\frac{2\pi}{3}, 0)$, which is reached at $p = 1$. The final state with anantiferromagnetic long-range order can be conceived as four interpenetratingsublattices with the $120^\circ$ spin structure on each of them. Obtainedresults are used for interpretation of the incommensurate magnetic orderingobserved in NiGa$_2$S$_4$.

Magnetic phase diagram of the spin-1 two-dimensional J1-J3 Heisenberg model on a triangular lattice