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Singular φ -Laplacian third-order BVPs with derivative dependance

Smaïl Djebali, Ouiza Saifi (2016)

Archivum Mathematicum

This work is devoted to the existence of solutions for a class of singular third-order boundary value problem associated with a φ -Laplacian operator and posed on the positive half-line; the nonlinearity also depends on the first derivative. The upper and lower solution method combined with the fixed point theory guarantee the existence of positive solutions when the nonlinearity is monotonic with respect to its arguments and may have a space singularity; however no Nagumo type condition is assumed....

Ski de fond

Alain Dufresnoy (1983/1984)

Séminaire de théorie spectrale et géométrie

Slant Hankel operators

Subhash Chander Arora, Ruchika Batra, M. P. Singh (2006)

Archivum Mathematicum

In this paper the notion of slant Hankel operator K ϕ , with symbol ϕ in L , on the space L 2 ( 𝕋 ) , 𝕋 being the unit circle, is introduced. The matrix of the slant Hankel operator with respect to the usual basis { z i : i } of the space L 2 is given by α i j = a - 2 i - j , where i = - a i z i is the Fourier expansion of ϕ . Some algebraic properties such as the norm, compactness of the operator K ϕ are discussed. Along with the algebraic properties some spectral properties of such operators are discussed. Precisely, it is proved that for an invertible...

Slowly oscillating perturbations of periodic Jacobi operators in l²(ℕ)

Marcin Moszyński (2009)

Studia Mathematica

We prove that the absolutely continuous part of the periodic Jacobi operator does not change (modulo unitary equivalence) under additive perturbations by compact Jacobi operators with weights and diagonals defined in terms of the Stolz classes of slowly oscillating sequences. This result substantially generalizes many previous results, e.g., the one which can be obtained directly by the abstract trace class perturbation theorem of Kato-Rosenblum. It also generalizes several results concerning perturbations...

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