Abstract In this paper, we study the spectrum of the fractional Laplace operator with sign-changing weight and show that there exist two simple, isolated principal eigenvalues λ 1 + and… Click to show full abstract
Abstract In this paper, we study the spectrum of the fractional Laplace operator with sign-changing weight and show that there exist two simple, isolated principal eigenvalues λ 1 + and λ 1 − . By use of the obtained spectrum results, we study the existence, multiplicity, and nonexistence of constant sign solutions to corresponding nonlinear problems according to the asymptotic behavior of nonlinear term f at 0, ∞, and whether f possesses zeros in R ∖ { 0 } . As far as we know, the spectral results presented here are new,and the rest theorems partially generalize the corresponding ones in the literature.
               
Click one of the above tabs to view related content.