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Spectrum and constant sign solutions for a fractional Laplace problem with sign-changing weight

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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.

Keywords: constant sign; fractional laplace; sign solutions; sign; sign changing; changing weight

Journal Title: Journal of Mathematical Analysis and Applications
Year Published: 2020

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