Eigenvalue Problem Of Fractional Laplace Operator With Indefinite Weight Function

Differential operator is one of the most basic unbounded operators in lin-ear operators, which has been widely applied in mathematical physics and other subjects. The eigenvalues and eigenfunctions of linear differential operators are one of the cores of the operator theory and the basis of the corresponding nonlin-ear problems. The dissertation mainly discusses the eigenvalue problems of the fractional Laplace operator with indefinite weight function under the bounded domain (?) existence results of eigenvalue sequence of the above problem are obtained, espe-cially we prove the first eigenvalue ?1 is simple, and is the only eigenvalue whose corresponding eigenfunction is definite. Then under the assumption that the weight function is a bounded measurable function, we discusses the existence of eigenvalue whose eigenfunction is negative, and the conclusion narrow the range of non-negative eigenfunction corresponding to the eigenvalue. The main results partially improve the known results about Yang et al. [Int. J. Bifur. Chaos],Servadei et al. [Discrete Contin. Dyn. Sys. 2013] and Brown et al [J. Math.Anal. Appl. 1980].