Stability of triangular libration points in a planar restricted elliptic three body problem in cases of double resonances

•Stability of triangular libration points in cases of double resonances is investigated.•The fourth-order double resonance provides formal stability.•The third- and fourth-order resonances provide boundedness of motions.

Stability of triangular libration points in a planar restricted elliptic three-body problem is investigated for two sets of parameters corresponding to the cases of double resonances. These positions are shown to be formally stable in the case of the fourth-order double resonance. When a weak third-order and a strong fourth-order resonances occur in the system, any motion of an approximate autonomous system is found to be bounded if initial conditions are sufficiently close to the unperturbed motion. Boundedness domain estimate is obtained.