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Self-adjoint boundary problems for the equation $y^{(4)}-lambdarho y=0$ with generalized derivative $rhoin W_2^{-1}[0,1]$ of self-similar Cantor type function as a weight are considered. Using the oscillating properties of the eigenfunctions, the spectral asymptotics are made more precise then in previous papers.
The present paper deals with the spectral and the oscillation properties of a linear pencil $A-lambda B$. Here $A$ and $B$ are linear operators generated by the differential expressions $(py)$ and $-y+ cry$, respectively. In particular, it is shown t
In this paper we study a family of operators dependent on a small parameter $epsilon > 0$, which arise in a problem in fluid mechanics. We show that the spectra of these operators converge to N as $epsilon to 0$, even though, for fixed $epsilon > 0$, the eigenvalue asymptotics are quadratic.
In this expository article some spectral properties of self-adjoint differential operators are investigated. The main objective is to illustrate and (partly) review how one can construct domains or potentials such that the essential or discrete spect
For the Schrodinger equation $-d^2 u/dx^2 + q(x)u = lambda u$ on a finite $x$-interval, there is defined an asymmetry function $a(lambda;q)$, which is entire of order $1/2$ and type $1$ in $lambda$. Our main result identifies the classes of square-in
We investigate the instability index of the spectral problem $$ -c^2y + b^2y + V(x)y = -mathrm{i} z y $$ on the line $mathbb{R}$, where $Vin L^1_{rm loc}(mathbb{R})$ is real valued and $b,c>0$ are constants. This problem arises in the study of stab