Before revision:  Analytical solutions are also obtained for these QEVPs. Moreover , we generalize the eigenvector-eigenvalue identity (rediscovered and coined recently for MEVPs) for GMEVPs and derive some trigonometric identities . Possible generalizations and applications to the design of better numerical methods for solving partial differential equations are discussed .
After revision:  Analytical solutions are also obtained for some polynomial eigenvalue problems (PEVPs). Lastly , we generalize the eigenvector-eigenvalue identity (rediscovered and coined recently for MEVPs) for GMEVPs and derive some trigonometric identities . Possible generalizations and applications to the design of better numerical methods for solving partial differential equations are discussed .