Singular nonlinear elliptic equations in .
This work is devoted to the existence of solutions for a class of singular third-order boundary value problem associated with a -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....
In this paper the notion of slant Hankel operator , with symbol in , on the space , being the unit circle, is introduced. The matrix of the slant Hankel operator with respect to the usual basis of the space is given by , where is the Fourier expansion of . Some algebraic properties such as the norm, compactness of the operator are discussed. Along with the algebraic properties some spectral properties of such operators are discussed. Precisely, it is proved that for an invertible...
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...