  This article provides an insight into several open problems in the quest for
novel modes of excitation in nuclei with isospin asymmetry, deformation and
finite temperature characteristic in stellar environment. Major unsolved
problems include the nature of pygmy dipole resonances, the quest for various
multipole and spin-isospin excitations both in neutron-rich and proton
drip-line nuclei mainly driven by loosely bound nucleons, excitations in
unstable deformed nuclei and evolution of their properties with the shape phase
transition. Exotic modes of excitation in nuclei at finite temperatures
characteristic for supernova evolution present open problems with possible
impact in modeling astrophysically relevant weak interaction rates. All these
issues challenge self-consistent many body theory frameworks at the frontiers
of on-going research, including nuclear energy density functionals, both
phenomenological and constrained by the strong interaction physics of QCD,
models based on low-momentum two-nucleon interaction V_{low-k} and correlated
realistic nucleon-nucleon interaction V_{UCOM}, supplemented by three-body
force, as well as two-nucleon and three-nucleon interactions derived from the
chiral effective field theory. Joined theoretical and experimental efforts,
including research with radioactive isotope beams, are needed to provide
insight into dynamical properties of nuclei away from the valley of stability,
involving the interplay of isospin asymmetry, deformation and finite
temperature.
