## 1 Introduction  
The advent of Bose-Einstein condensates (BECs) in \({}^{52}\)Cr [1; 2], \({}^{164}\)Dy [3; 4] and \({}^{168}\)Er [5] accompanied by long-range dipole-dipole (DD) interactions superimposed on the contact inter-atomic collisions has impacted the investigation of ultracold quantum gases [6]. The anisotropic character and long-range nature of DD interactions endows the dipolar BECs (DBECs) with several distinct features such as the subordination of stability on the trap geometry [1; 2], roton-maxon character of the excitation spectrum [7; 8], new dispersion relations for elementary excitations [9; 10], novel quantum phases [11; 12], explicit [13; 14] and hidden vortices [15], specific vortex-antivortex pairs [16], anisotropic multidimensional solitons [17; 18], quantum droplets stabilized by beyond-mean-field effects [19; 20; 21], etc. The above phenomena arise due to the interplay between the contact \(s\)-wave interactions and the dipolar attraction or repulsion [22]. Tuning contact interactions by means of the Feshbach resonance is an important tool in analyzing the properties of DBECs [7; 8]. In particular, DBECs with pure long-range interactions can be made by tuning the contact interactions to zero. The theoretical description of a dilute weakly interacting DBEC is based on the Gross-Pitaevskii (GP) equation with the nonlocal DD-interaction term [1; 23; 24; 25]. In particular, the combination of local and nonlocal terms in the GP equation can support various species of bright and dark matter-wave solitons. In the alkali BECs, bright solitons exist when the negative (attractive) contact interaction exactly balances the dispersion (kinetic-energy) term [26; 27]. In DBEC, the nonlocal DD interaction term may reinforce local ones originating from the \(s\)-wave contact interaction. DD interactions are strongest in the atomic condensatesof lanthanide series elements such as \({}^{168}\)Er and \({}^{164}\)Dy. Long-range interactions also play a crucially important role in optics of nonlocal media, where they induce modulational instability, solitons, and vortices [28; 29]. The DD interactions in BECs can support bright solitons even for the positive (repulsive) contact interaction [23]. Following the scheme of the stabilization of the inverted (Kapitza) pendulum [30], scenarios for stabilization of two-dimensional (2D) optical [31] and matter-waves [32; 33; 34] by means of the \"nonlinearity management\" [35], i.e., the cubic nonlinearity periodically switching between self-attraction and repulsion, have been elaborated. This concept has been subsequently applied to 3D vortex solitons [32; 34] and extended to the model containing the three-body interaction [36] and quantum fluctuations [37]. The stabilization of self-repulsive BECs with periodically varying higher-order interactions has been explored recently [38]. The investigation of spatial and temporally varying nonlinearities has also drawn considerable interest in optics [39; 40; 41; 31] and other BEC settings [42; 43; 44; 45; 46; 47; 48; 49; 50]. The above investigations addressed systems with local interactions. Recently, the possibility of the stabilization of DBECs by temporal modulation of the contact interaction was demonstrated, too [51]. In the latter case, a potential minima necessary for self-trapping is found to be absent without the time-periodic modulation of the two- and three-body interaction. The current work primarily addresses this situation, attempting to stabilize DBECs by adding three-body terms to the binary interaction, cf. Refs. [52; 53; 54; 55; 56; 57]. As a result, the present work offers a simple protocol to stabilize multidimensional trapless DBECs. The organization of the paper is as follows. In Section 2, we set the mean-field model based on the nonlocal GP equation. Then, we introduce the variational method in Section 3 and demonstrate the stabilization of a trapless DBEC without time-periodic modulation of the contact interaction.