Abstract: The study of nuclear isoscalar giant monopole resonance (ISGMR) is an important way to constrain nuclear incompressibility coefficient K_\infty, which provides important information for the understanding of nuclear astrophysics phenomena. At present, there is a serious discrepancy in the unified descriptions of the ISGMR in Pb and Sn isotopes, i.e., the so called "why is the equation of state for tin so soft?", which prevents us from the accurate determination of K_\infty. In this paper, we introduce the quasiparticle random phase approximation (QRPA) theory, which is commonly used in the study of nuclear giant resonances, and also the self-consistent quasiparticle-vibration coupling (QPVC) theory based on the QRPA. The researches for the current issue within QRPA and QRPA+QPVC theories are reviewed, especially for the important role of the QPVC effects in achieving a unified description of ISGMR: a unified descriptions of ISGMR in Sn and Pb can be achieved with the QPVC effects, the problem "why is the equation of state for tin so soft?" can be solved, and the incompressibility coefficient K_\infty is constrained. Besides, based on the self-consistent QPVC theory, we further studied the electric monopole excitation strength disctributions in the neutron-rich Sn isotopes^{134, 140}Sn.