Existence Theorems of Operator's Eigenvalue and Eigenvectors
Jiandong Yin · Journal of Nanchang University · 2010
By using properties of 1-set-contractive mappin's topology degree proposed in W.V.petryshyr(1972) and properties of semi-closed 1-set-contractive mappings,this paper investigates exstence problems of a class of operator's eigenvalue and eigenvectors in Banach spaces.Under some mild conditions,at least there exist one eigenvalue greater than one and the corresponding eigenvector on the boundary of the domain.These new results can be used to investigate solution problems of varieties of nonlinear operator equations further.