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

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

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

The theoretical results relevant to the vibration modes of Timoshenko beams are here used as benchmarks for assessing the correctness of the numerical values...

Structural dynamics | 35C05 | Timoshenko beam | 34L15 | 35L25 | 34L10 | Primary 74K10 | Secondary 70J10 | 74H05 | 74H45 | 70J30 | vibration analysis | frequency spectrum | isogeometric analysis | MATHEMATICS, APPLIED | DEEP CURVED BEAMS | MODEL | IDENTIFICATION | TRANSVERSE VIBRATIONS | HOMOGENIZATION | NURBS | MECHANICS | BONE TISSUE | SARDINIA RADIO TELESCOPE | POSTBUCKLING BEHAVIOR | B-SPLINE INTERPOLATION | Fourier transforms | Finite element method | Permissible error | Accuracy | Mathematical analysis | Vibration mode | Error detection | Mathematical models | Timoshenko beams

Structural dynamics | 35C05 | Timoshenko beam | 34L15 | 35L25 | 34L10 | Primary 74K10 | Secondary 70J10 | 74H05 | 74H45 | 70J30 | vibration analysis | frequency spectrum | isogeometric analysis | MATHEMATICS, APPLIED | DEEP CURVED BEAMS | MODEL | IDENTIFICATION | TRANSVERSE VIBRATIONS | HOMOGENIZATION | NURBS | MECHANICS | BONE TISSUE | SARDINIA RADIO TELESCOPE | POSTBUCKLING BEHAVIOR | B-SPLINE INTERPOLATION | Fourier transforms | Finite element method | Permissible error | Accuracy | Mathematical analysis | Vibration mode | Error detection | Mathematical models | Timoshenko beams

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

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

Journal Article

Journal of Inequalities and Applications, ISSN 1025-5834, 12/2018, Volume 2018, Issue 1, pp. 1 - 11

A Lyapunov-type inequality is established for the anti-periodic fractional boundary value problem (CDaα,ψu)(x)+f(x,u(x))=0,a eigenvalues | 26D10 | Analysis | ψ -Caputo fractional derivative | 34L15 | Mathematics, general | Mathematics | Applications of Mathematics | Lyapunov-type inequalities | anti-periodic fractional boundary value problem | 34A08 | ψ-Caputo fractional derivative | Eigenvalues | Boundary value problems | Research

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

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

This paper is concerned with the periodic principal eigenvalue k(lambda)(mu) associated with the operator -d(2)/dx(2) - 2 lambda d/dx - mu(x) - lambda(2),...

Eigenvalue optimization | Reaction-diffusion equations | Schwarz rearrangement | Nnonsymmetric operator | MATHEMATICS, APPLIED | FRAGMENTED ENVIRONMENT MODEL | BIOLOGICAL INVASIONS | eigenvalue optimization | DIFFUSIVE LOGISTIC EQUATIONS | nonsymmetric operator | PERSISTENCE | FORMULA | POPULATION-MODELS | WAVES | INDEFINITE WEIGHTS | ELLIPTIC-EQUATIONS | reaction-diffusion equations | PROPAGATION | Analysis of PDEs | Mathematics | Optimization and Control

Eigenvalue optimization | Reaction-diffusion equations | Schwarz rearrangement | Nnonsymmetric operator | MATHEMATICS, APPLIED | FRAGMENTED ENVIRONMENT MODEL | BIOLOGICAL INVASIONS | eigenvalue optimization | DIFFUSIVE LOGISTIC EQUATIONS | nonsymmetric operator | PERSISTENCE | FORMULA | POPULATION-MODELS | WAVES | INDEFINITE WEIGHTS | ELLIPTIC-EQUATIONS | reaction-diffusion equations | PROPAGATION | Analysis of PDEs | Mathematics | Optimization and Control

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

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

The present paper deals with non-real eigenvalues of regular nonlocal indefinite Sturm–Liouville problems. The existence of non-real eigenvalues of indefinite...

34B24 | 34L15 | Mathematics | 47B50 | Non-real eigenvalue | Ordinary Differential Equations | Analysis | Nonlocal potential | Difference and Functional Equations | Approximations and Expansions | Mathematics, general | Indefinite Sturm–Liouville problem | A priori bounds | Partial Differential Equations | Eigenvalues | Boundary conditions | Upper bounds | Differential equations | Eigen values

34B24 | 34L15 | Mathematics | 47B50 | Non-real eigenvalue | Ordinary Differential Equations | Analysis | Nonlocal potential | Difference and Functional Equations | Approximations and Expansions | Mathematics, general | Indefinite Sturm–Liouville problem | A priori bounds | Partial Differential Equations | Eigenvalues | Boundary conditions | Upper bounds | Differential equations | Eigen values

Journal Article

Journal of Scientific Computing, ISSN 0885-7474, 2/2019, Volume 78, Issue 2, pp. 1231 - 1249

In this paper, a shape optimization problem corresponding to the p-Laplacian operator is studied. Given a density function in a rearrangement class generated...

Eigenvalue optimization | Rearrangement algorithm | Computational Mathematics and Numerical Analysis | Algorithms | p -Laplacian | Theoretical, Mathematical and Computational Physics | Mathematical and Computational Engineering | 34L16 | 34L15 | Mathematics | 49M37 | 35P30 | p-Laplacian | MATHEMATICS, APPLIED | OPTIMIZATION PROBLEM | SYMMETRY | MINIMIZATION | 1ST EIGENVALUE | CONFIGURATIONS

Eigenvalue optimization | Rearrangement algorithm | Computational Mathematics and Numerical Analysis | Algorithms | p -Laplacian | Theoretical, Mathematical and Computational Physics | Mathematical and Computational Engineering | 34L16 | 34L15 | Mathematics | 49M37 | 35P30 | p-Laplacian | MATHEMATICS, APPLIED | OPTIMIZATION PROBLEM | SYMMETRY | MINIMIZATION | 1ST EIGENVALUE | CONFIGURATIONS

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

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

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

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

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

In this paper, localization theorems for left and right eigenvalues of a quaternion matrix are presented. Some differences between quaternion matrices and...

Computational Mathematics and Numerical Analysis | 12E15 | Quaternion matrix | 34L15 | Mathematics | Theory of Computation | Left and right eigenvalues | 15A18 | Mathematics of Computing | Gerschgorin theorems | Split quaternion matrix | 15A66 | Mathematical and Computational Engineering | MATHEMATICS | EIGENVALUES | MATHEMATICS, APPLIED | ROTATIONS | Quaternions | Eigenvalues | Theorems

Computational Mathematics and Numerical Analysis | 12E15 | Quaternion matrix | 34L15 | Mathematics | Theory of Computation | Left and right eigenvalues | 15A18 | Mathematics of Computing | Gerschgorin theorems | Split quaternion matrix | 15A66 | Mathematical and Computational Engineering | MATHEMATICS | EIGENVALUES | MATHEMATICS, APPLIED | ROTATIONS | Quaternions | Eigenvalues | Theorems

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

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

We analyze eigenvalues emerging from thresholds of the essential spectrum of one-dimensional Dirac operators perturbed by complex and non-symmetric potentials....

34L40 | Non-self-adjoint Dirac operator | Lieb–Thirring inequalities | Complex potential | Armchair graphene nanoribbons | Theoretical, Mathematical and Computational Physics | Complex Systems | 34L15 | Physics | Geometry | 35P15 | 81Q12 | Birman–Schwinger principle | Damped wave equation | Group Theory and Generalizations | BOUNDS | Lieb-Thirring inequalities | Birman-Schwinger principle | JACOBI MATRICES | PHYSICS, MATHEMATICAL | RESONANCES | SCHRODINGER-OPERATORS | Graphene | Graphite | Mathematics - Spectral Theory

34L40 | Non-self-adjoint Dirac operator | Lieb–Thirring inequalities | Complex potential | Armchair graphene nanoribbons | Theoretical, Mathematical and Computational Physics | Complex Systems | 34L15 | Physics | Geometry | 35P15 | 81Q12 | Birman–Schwinger principle | Damped wave equation | Group Theory and Generalizations | BOUNDS | Lieb-Thirring inequalities | Birman-Schwinger principle | JACOBI MATRICES | PHYSICS, MATHEMATICAL | RESONANCES | SCHRODINGER-OPERATORS | Graphene | Graphite | Mathematics - Spectral Theory

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

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

A finite discrete graph is turned into a quantum (metric) graph once a finite length is assigned to each edge and the one-dimensional Laplacian is taken to be...

Mathematical Methods in Physics | Theoretical, Mathematical and Computational Physics | Quantum Physics | Dynamical Systems and Ergodic Theory | Classical and Quantum Gravitation, Relativity Theory | Physics | Elementary Particles, Quantum Field Theory | EIGENVALUES | METRIC GRAPHS | PHYSICS, MULTIDISCIPLINARY | PHYSICS, MATHEMATICAL | STATISTICS | PHYSICS, PARTICLES & FIELDS

Mathematical Methods in Physics | Theoretical, Mathematical and Computational Physics | Quantum Physics | Dynamical Systems and Ergodic Theory | Classical and Quantum Gravitation, Relativity Theory | Physics | Elementary Particles, Quantum Field Theory | EIGENVALUES | METRIC GRAPHS | PHYSICS, MULTIDISCIPLINARY | PHYSICS, MATHEMATICAL | STATISTICS | PHYSICS, PARTICLES & FIELDS

Journal Article

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