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.
Cuesta,Minimax theorems onC 1 manifolds via Ekeland variational principle, Abstr
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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.