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Applicable Analysis, ISSN 0003-6811, 09/2019, Volume 98, Issue 12, pp. 2145 - 2177
In this paper, we study the spectrum of the one-dimensional vibrating free rod equation under tension or compression . The eigenvalues as functions of the... 
fourth order | Secondary: 34L10 | cascading | Primary: 34L15 | avoided crossings | Bi-Laplacian | EIGENVALUES | MATHEMATICS, APPLIED | Eigenvalues | Eigenvectors | Line spectra | Cascading | Eigen values
Journal Article
Mathematische Zeitschrift, ISSN 0025-5874, 6/2016, Volume 283, Issue 1, pp. 339 - 348
Let $$\lambda _j$$ λ j be the jth eigenvalue of Sturm–Liouville systems with separated boundary conditions, we build up the Hill-type formula, which represent... 
Hamiltonian systems | 47E05 | Sturm–Liouville systems | 34B24 | Trace formula | 34L15 | Mathematics, general | Mathematics | Hill-type formula
Journal Article
ZAMM ‐ Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik, ISSN 0044-2267, 10/2016, Volume 96, Issue 10, pp. 1220 - 1244
Journal Article
Letters in Mathematical Physics, ISSN 0377-9017, 11/2019, Volume 109, Issue 11, pp. 2491 - 2512
Ground-state eigenfunctions of Schrödinger operators can often be chosen positive. We analyse to which extent this is true for quantum graphs—differential... 
Geometry | 35R30 | Theoretical, Mathematical and Computational Physics | Complex Systems | 34L15 | Ground state | Group Theory and Generalizations | Quantum graphs | Positivity preserving semigroups | Physics
Journal Article
Abstract and Applied Analysis, ISSN 1085-3375, 03/2004, Volume 2004, Issue 2, pp. 147 - 153
We present sharp lower bounds for eigenvalues of the one-dimensional p -Laplace operator. The method of proof is rather elementary, based on a suitable... 
34L15 | 34L30
Journal Article
Journal of Inequalities and Applications, ISSN 1025-5834, 12/2018, Volume 2018, Issue 1, pp. 1 - 11
Journal Article
Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas, ISSN 1578-7303, 1/2019, Volume 113, Issue 1, pp. 171 - 179
In this work we derive a Lyapunov-type inequality for a what may be called “sequential fractional right-focal boundary value problem”. A bound for the possible... 
Lyapunov inequality | Focal boundary conditions | Primary 34A08 | 26D10 | Theoretical, Mathematical and Computational Physics | Eigenvalues | 34L15 | Mathematics, general | Mathematics | Applications of Mathematics | Fractional derivatives | MATHEMATICS | Boundary value problems
Journal Article
SIAM Journal on Mathematical Analysis, ISSN 0036-1410, 2009, Volume 41, Issue 6, pp. 2388 - 2406
Journal Article
Fractional Calculus and Applied Analysis, ISSN 1311-0454, 02/2017, Volume 20, Issue 1, pp. 284 - 291
In this note we present a Lyapunov-type inequality for a fractional boundary value problem with anti-periodic boundary conditions, that we show to be a... 
Primary 34A08 | fractional derivatives | eigenvalues | Secondary 26D10 | boundary value problems | 34L15 | Lyapunov’s inequality | Lyapunov's inequality | MATHEMATICS | MATHEMATICS, APPLIED | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | Inequalities (Mathematics) | Boundary value problems | Analysis
Journal Article
Boundary Value Problems, ISSN 1687-2770, 12/2019, Volume 2019, Issue 1, pp. 1 - 12
Journal Article
Journal of Scientific Computing, ISSN 0885-7474, 2/2019, Volume 78, Issue 2, pp. 1231 - 1249
Journal Article
Journal of Inequalities and Applications, ISSN 1025-5834, 2018, Volume 2018, Issue 1, pp. 1 - 11
In this paper analogues of Sobolev inequalities for compact and connected metric graphs are derived. As a consequence of these inequalities, a lower bound,... 
Laplace operator | Quantum graphs | Isoperimetric inequalities | Metric graphs | Sobolev inequalities | LAPLACIAN | MATHEMATICS | CHAOS | MATHEMATICS, APPLIED | SPECTRAL PROPERTIES | OPERATORS | Eigenvalues | Lower bounds | Graphs | Inequalities | 35P15 | 81Q35 | 34L15 | Research | 81Q10
Journal Article
Integral Equations and Operator Theory, ISSN 0378-620X, 7/2013, Volume 76, Issue 3, pp. 381 - 401
For a self-adjoint Laplace operator on a finite, not necessarily compact metric graph lower and upper bounds on each of the negative eigenvalues are derived.... 
negative eigenvalues of self-adjoint Laplacians | eigenvalue zero | Secondary 35J05 | Analysis | Differential operators on metric graphs | 34L15 | Mathematics | Primary 34B45 | lower bounds on the spectrum | MATHEMATICS | VARIATIONAL-PRINCIPLES
Journal Article
Mathematische Annalen, ISSN 0025-5831, 9/2013, Volume 357, Issue 1, pp. 185 - 213
Ordinary and partial differential operators with an indefinite weight function can be viewed as bounded perturbations of non-negative operators in Krein... 
34B24 | 34L15 | Mathematics, general | 46C20 | Mathematics | 47B50 | 47F05 | MATHEMATICS | DEFINITIZABLE OPERATORS | SELF-ADJOINT OPERATORS | COMPACT PERTURBATIONS | STURM-LIOUVILLE OPERATORS | KREIN SPACE | Invisibility | Analysis
Journal Article
Bulletin of the Iranian Mathematical Society, ISSN 1017-060X, 12/2019, Volume 45, Issue 6, pp. 1755 - 1775
In this paper, we consider the problem of computing the c-numerical range numerically for block differential operators, particularly these of Schrödinger type,... 
65L15 | 34L15 | 47A12 | Mathematics | Block operator matrices | Operator matrices | Hain–Lüst operator | 15A22 | c-Numerical range | Schrödinger operator | Finite difference | Mathematics, general | Stokes operator | 65L12 | MATHEMATICS | Hain-Lust operator | Schrodinger operator
Journal Article
Journal of Applied Mathematics and Computing, ISSN 1598-5865, 10/2018, Volume 58, Issue 1, pp. 323 - 334
Journal Article
Integral Equations and Operator Theory, ISSN 0378-620X, 3/2014, Volume 78, Issue 3, pp. 383 - 405
We study one-dimensional Schrödinger operators with complex measures as potentials and present an improved criterion for absence of eigenvalues which involves... 
34L40 | 81Q12 | Analysis | 34L15 | Mathematics | 81Q10 | Schrödinger operators | quasiperiodic potential | eigenvalue problem | SPECTRAL THEORY | MATHEMATICS | Schrodinger operators
Journal Article
Letters in Mathematical Physics, ISSN 0377-9017, 7/2018, Volume 108, Issue 7, pp. 1757 - 1778
Journal Article
Forum Mathematicum, ISSN 0933-7741, 05/2017, Volume 29, Issue 3, pp. 575 - 579
In this paper, we look for an explicit lower bound of the smallest value of the spectrum for a relativistic Schrödinger operator in a domain of the Euclidean... 
covering multiplicity | 47A07 | 35P15 | Fractional-capacity | fractional Sobolev inequality | 34L05 | quadratic forms | 34L15 | 81Q10 | 47A40 | Covering multiplicity | Fractional Sobolev inequality | Fractional-Capacity | Quadratic forms | MATHEMATICS | MATTER | MATHEMATICS, APPLIED | POSITIVITY CRITERIA | DISCRETENESS | STABILITY
Journal Article
Annales Henri Poincaré, ISSN 1424-0637, 10/2017, Volume 18, Issue 10, pp. 3269 - 3323
Journal Article
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