On the monotonicity of nonnegative solutions and the uniqueness of eigenvalues
On the periodic spectrum of the 1-dimensional Schrödinger operator.
On the resonance problem for the order ordinary differential equations, Fučík’s spectrum
On the sensitivity of the matrix exponential problem
On the singular spectrum for adiabatic quasiperiodic Schrödinger operators.
On the singular spectrum of discrete Schrödinger operator
On the solution of a differential equation occurring in the problem of heat convection in laminar flow through a tube with slip-flow.
On the Solutions of (ry')' + qy = f.
On the spectra of non-selfadjoint differential operators and their adjoints in direct sum spaces.
On the spectrum of a discrete non-Hermitian quantum system.
On the spectrum of non-selfadjoint differential operators.
On the spectrum of the operator which is a composition of integration and substitution
Let ϕ: [0,1] → [0,1] be a nondecreasing continuous function such that ϕ(x) > x for all x ∈ (0,1). Let the operator be defined on L₂[0,1]. We prove that has a finite number of nonzero eigenvalues if and only if ϕ(0) > 0 and ϕ(1-ε) = 1 for some 0 < ε < 1. Also, we show that the spectral trace of the operator always equals 1.
On two-dimensional finite-gap potential Schrödinger and Dirac operators with singular spectral curves.
On weighted positivity of ordinary differential operators.
One-dimensional Schrödinger operators with interactions singular on a discrete set.
One-dimensional Schrödinger operators with local point interactions.
Opial's type inequalities on time scales and some applications
We prove some new Opial type inequalities on time scales and employ them to prove several results related to the spacing between consecutive zeros of a solution or between a zero of a solution and a zero of its derivative for second order dynamic equations on time scales. We also apply these inequalities to obtain a lower bound for the smallest eigenvalue of a Sturm-Liouville eigenvalue problem on time scales. The results contain as special cases some results obtained for second order differential...
Optimal conditions for maximum and antimaximum principles of the periodic solution problem.
Optimization of the principal eigenvalue of the one-dimensional Schrödinger operator.
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