The excitation phenomena in unstable nuclei are investigated in the framework of the relativistic quasiparticle random-phase approximation (RQRPA) in the relativistic Hartree-Bogoliubov model (RHB) which is extended to include effective interactions with explicit density-dependent meson-nucleon couplings. The properties of the pygmy dipole resonance (PDR) are examined in 132Sn and within isotopic chains, showing that already at moderate proton-neutron asymmetry the PDR peak energy is located above the neutron emission threshold. A method is suggested for determining the size of the neutron skin within an isotopic chain, based on the measurement of the excitation energies of the Gamow-Teller resonance relative to the isobaric analog state. In addition, for the first time the relativistic RHB + RQRPA model, with tensor ? meson-nucleon couplings, is employed in calculations of ?-decay half-lives of nuclei of the relevance for the r-process.