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.
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2026 2verdicts
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A fractional logarithmic p-Laplacian operator is defined by differentiating the fractional p-Laplacian, yielding an integral form with a log term, and applied to prove inequalities and eigenvalue results.
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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.
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On the fractional logarithmic $p$-Laplacian
A fractional logarithmic p-Laplacian operator is defined by differentiating the fractional p-Laplacian, yielding an integral form with a log term, and applied to prove inequalities and eigenvalue results.