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Spectral properties of Sturm-Liouville operators on infinite metric graphs
Yihan Liu, Jun Yan, Jia Zhao
This paper mainly deals with the Sturm-Liouville operator \begin{equation*} \mathbf{H}=\frac{1}{w(x)}\left( -\frac{\mathrm{d}}{\mathrm{d}x}p(x)\frac{ \mathrm{d}}{\mathrm{d}x}+q(x)\…
Dependence of Solutions and Eigenvalues of Third Order Linear Measure Differential Equations on Measures
Yixuan Liu, Guoliang Shi, Jun Yan
This paper deals with a complex third order linear measure differential equation \begin{equation*} i\mathrm{d}\left( y^{\prime }\right) ^{\bullet }+2iq\left( x\right) y^{\prime }\m…
Inverse spectral problems for non-self-adjoint Sturm-Liouville operators with discontinuous boundary conditions
Jun Yan, Guoliang Shi
This paper deals with the inverse spectral problem for a non-self-adjoint Sturm-Liouville operator with discontinuous conditions inside the interval. We obtain that if the potentia…
Multiplicities of Eigenvalues of the Diffusion Operator with Random Jumps from the Boundary
Jun Yan, Guoliang Shi
This paper deals with a non-self-adjoint differential operator which is associated with a diffusion process with random jumps from the boundary. Our main result is that the algebra…
Eigenvalues of Sturm-Liouville Operators with Distributional Potentials
Jun Yan, Guoliang Shi, Jia Zhao
We introduce a novel approach for dealing with eigenvalue problems of Sturm-Liouville operators generated by the differential expression \begin{equation*} Ly=\frac{1}{r}\left( -(p\…