Monotonicity of eigenvalues of the fractional $p$-Laplacian with singular weights
Copyright policy )Monotonicity of eigenvalues of the fractional $p$-Laplacian with singular weights
We study a nonlinear, nonlocal eigenvalue problem driven by the fractional $p$-Laplacian with an indefinite, singular weight chosen in an optimal class. We prove the existence of an unbounded sequence of positive variational eigenvalues and alternative characterizations of the first and second eigenvalues. Then, by means of such characterizations, we prove strict decreasing monotonicity of such eigenvalues with respect to the weight function.
- University of Cagliari Italy
Mathematics - Analysis of PDEs, Boundary value problems for second-order elliptic equations, eigenvalue problems, fractional \(p\)-Laplacian, FOS: Mathematics, 35P30, 35R11, Nonlinear eigenvalue problems and nonlinear spectral theory for PDEs, Fractional p-Laplacian; Eigenvalue problems; Singular weights, Quasilinear elliptic equations with \(p\)-Laplacian, singular weights, Analysis of PDEs (math.AP)
Mathematics - Analysis of PDEs, Boundary value problems for second-order elliptic equations, eigenvalue problems, fractional \(p\)-Laplacian, FOS: Mathematics, 35P30, 35R11, Nonlinear eigenvalue problems and nonlinear spectral theory for PDEs, Fractional p-Laplacian; Eigenvalue problems; Singular weights, Quasilinear elliptic equations with \(p\)-Laplacian, singular weights, Analysis of PDEs (math.AP)
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