Existence of an unbounded sequence of Lusternik-Schnirelmann eigenvalues is shown for the logarithmic Laplacian with indefinite weights; the first eigenvalue is simple with constant-sign eigenfunction, higher ones change sign, and nodal inequalities plus monotonicity hold.
Iannizzotto,Monotonicity of eigenvalues of the fractionalp-Laplacian with singular weights, Topol
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Spectral Properties of the Logarithmic Laplacian with Indefinite Weights
Existence of an unbounded sequence of Lusternik-Schnirelmann eigenvalues is shown for the logarithmic Laplacian with indefinite weights; the first eigenvalue is simple with constant-sign eigenfunction, higher ones change sign, and nodal inequalities plus monotonicity hold.