Journal of the London Mathematical Society, ISSN 0024-6107, 06/2019, Volume 99, Issue 3, pp. 831 - 852

In this paper, we study the mixed dispersion fourth‐order nonlinear Helmholtz equation Δ2u−βΔu+αu=Γ|u|p−2uinRN,for positive, bounded and ZN‐periodic functions...

35J35 (primary) | 35J05 (secondary) | MATHEMATICS | REGULARITY | STABILITY | SCHRODINGER-EQUATION | DUAL VARIATIONAL-METHODS | STANDING WAVES | GLOBAL WELL-POSEDNESS | SCATTERING | Mathematics - Analysis of PDEs

35J35 (primary) | 35J05 (secondary) | MATHEMATICS | REGULARITY | STABILITY | SCHRODINGER-EQUATION | DUAL VARIATIONAL-METHODS | STANDING WAVES | GLOBAL WELL-POSEDNESS | SCATTERING | Mathematics - Analysis of PDEs

Journal Article

International Mathematics Research Notices, ISSN 1073-7928, 03/2017, Volume 2017, Issue 5, pp. 1487 - 1503

In this article we find the sharp error term in an L-2-three circles theorem for discrete harmonic functions on Z(2). The proof is highly indirect due to...

MATHEMATICS

MATHEMATICS

Journal Article

Archiv der Mathematik, ISSN 0003-889X, 3/2019, Volume 112, Issue 3, pp. 305 - 311

.... Primary 35P15; Secondary 35J05, 35J25, 35P20. Keywords. Dirichlet Laplacian, Eigenvalues, Faber–Krahn inequality, P´ olya’s conjecture. Let Ω be a bounded domain in R...

Dirichlet Laplacian | Secondary 35J05 | Eigenvalues | Pólya’s conjecture | Mathematics, general | Mathematics | Faber–Krahn inequality | 35P20 | 35J25 | Primary 35P15 | MATHEMATICS | Polya's conjecture | Faber-Krahn inequality | DOMAINS

Dirichlet Laplacian | Secondary 35J05 | Eigenvalues | Pólya’s conjecture | Mathematics, general | Mathematics | Faber–Krahn inequality | 35P20 | 35J25 | Primary 35P15 | MATHEMATICS | Polya's conjecture | Faber-Krahn inequality | DOMAINS

Journal Article

Annali di Matematica Pura ed Applicata (1923 -), ISSN 0373-3114, 8/2018, Volume 197, Issue 4, pp. 1227 - 1246

This paper deals with the following supercritical Hénon-type equation $$\begin{aligned} {\left\{ \begin{array}{ll} -\Delta u=|x|^\alpha |u|^{p_\alpha...

35J40 | Secondary 35J05 | Lyapunov–Schmidt reduction | Hénon-type equation | Mathematics, general | Mathematics | Primary 35J60 | Sign-changing bubble tower solutions | Information science

35J40 | Secondary 35J05 | Lyapunov–Schmidt reduction | Hénon-type equation | Mathematics, general | Mathematics | Primary 35J60 | Sign-changing bubble tower solutions | Information science

Journal Article

Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 11/2016, Volume 443, Issue 2, pp. 707 - 731

Mellin convolution equations acting in Bessel potential spaces are considered. The study is based upon two results. The first one concerns the interaction of...

Operator algebras | Fixed singularities | Fourier convolutions | Bessel potential spaces | Symbol | Mellin convolutions | MATHEMATICS | MATHEMATICS, APPLIED | STABILITY | PSEUDODIFFERENTIAL-OPERATORS | INTEGRAL-OPERATORS | Algebra | Mathematics - Functional Analysis

Operator algebras | Fixed singularities | Fourier convolutions | Bessel potential spaces | Symbol | Mellin convolutions | MATHEMATICS | MATHEMATICS, APPLIED | STABILITY | PSEUDODIFFERENTIAL-OPERATORS | INTEGRAL-OPERATORS | Algebra | Mathematics - Functional Analysis

Journal Article

Mathematical Physics, Analysis and Geometry, ISSN 1385-0172, 6/2017, Volume 20, Issue 2, pp. 1 - 24

In a previous paper, the authors introduced the idea of a symmetric pair of operators as a way to compute self-adjoint extensions of symmetric operators. In...

Graph energy | Theoretical, Mathematical and Computational Physics | Krein extension | 47B32 | 60H07. Secondary: 05C50 | 35J05 | Tomita-Takesaki theory | Graph Laplacian | Von Neumann algebra | 47B25 | Defect indices | Hilbert space | Applications of Mathematics | Resistance network | Malliavin derivative | 05C63 | Effective resistance | Essentially self-adjoint | Abstract Wiener space | Physics | Spectral graph theory | Stochastic integration | Geometry | Reproducing kernel | Unbounded linear operator | Symmetric pair | Spectral resolution | Type III factor | Gaussian fields | 47B15 | 46E22 | Analysis | Self-adjoint extension | Group Theory and Generalizations | Friedrichs extension | Malliavin calculus | Modular automorphism | Primary: 46L36 | MATHEMATICS, APPLIED | PHYSICS, MATHEMATICAL | NETWORKS | Algebra | Mathematics - Functional Analysis

Graph energy | Theoretical, Mathematical and Computational Physics | Krein extension | 47B32 | 60H07. Secondary: 05C50 | 35J05 | Tomita-Takesaki theory | Graph Laplacian | Von Neumann algebra | 47B25 | Defect indices | Hilbert space | Applications of Mathematics | Resistance network | Malliavin derivative | 05C63 | Effective resistance | Essentially self-adjoint | Abstract Wiener space | Physics | Spectral graph theory | Stochastic integration | Geometry | Reproducing kernel | Unbounded linear operator | Symmetric pair | Spectral resolution | Type III factor | Gaussian fields | 47B15 | 46E22 | Analysis | Self-adjoint extension | Group Theory and Generalizations | Friedrichs extension | Malliavin calculus | Modular automorphism | Primary: 46L36 | MATHEMATICS, APPLIED | PHYSICS, MATHEMATICAL | NETWORKS | Algebra | Mathematics - Functional Analysis

Journal Article

Journal of Evolution Equations, ISSN 1424-3199, 6/2014, Volume 14, Issue 2, pp. 477 - 497

For a finite not necessarily compact metric graph, one considers the differential expression $${-\frac{d^2}{d x^2}}$$ - d 2 d x 2 on each edge. The boundary...

47D06 | Secondary 35J05 | Analysis | Differential operators on metric graphs | 35K05 | Mathematics | Primary 34B45 | Quasi-contractive semigroups | Quasi-m-accretive Laplacians | MATHEMATICS | EIGENVALUES | MATHEMATICS, APPLIED

47D06 | Secondary 35J05 | Analysis | Differential operators on metric graphs | 35K05 | Mathematics | Primary 34B45 | Quasi-contractive semigroups | Quasi-m-accretive Laplacians | MATHEMATICS | EIGENVALUES | MATHEMATICS, APPLIED

Journal Article

Nonlinear Differential Equations and Applications NoDEA, ISSN 1021-9722, 4/2018, Volume 25, Issue 2, pp. 1 - 26

This paper considers a pair of coupled nonlinear Helmholtz equations $$\begin{aligned} {\left\{ \begin{array}{ll} -\,\Delta u - \mu u = a(x) \left(...

Dual variational methods | Mathematics | Nonlinear Helmholtz sytem | Primary 35J50 | Secondary 35J05 | Analysis | MATHEMATICS, APPLIED | EQUATION | Mathematics - Analysis of PDEs

Dual variational methods | Mathematics | Nonlinear Helmholtz sytem | Primary 35J50 | Secondary 35J05 | Analysis | MATHEMATICS, APPLIED | EQUATION | Mathematics - Analysis of PDEs

Journal Article

Constructive Approximation, ISSN 0176-4276, 4/2017, Volume 45, Issue 2, pp. 243 - 271

.... Keywords Bounded harmonic functions · Estimates of the gradient · The Khavinson problem · The Schwarz lemma Mathematics Subject Classi cation Primary 35B30; Secondary...

Estimates of the gradient | The Khavinson problem | Secondary 35J05 | Numerical Analysis | Analysis | Bounded harmonic functions | Primary 35B30 | Mathematics | The Schwarz lemma | MATHEMATICS | HARMONIC-FUNCTIONS

Estimates of the gradient | The Khavinson problem | Secondary 35J05 | Numerical Analysis | Analysis | Bounded harmonic functions | Primary 35B30 | Mathematics | The Schwarz lemma | MATHEMATICS | HARMONIC-FUNCTIONS

Journal Article

Archiv der Mathematik, ISSN 0003-889X, 3/2018, Volume 110, Issue 3, pp. 261 - 271

We introduce an analogue of Payne’s nodal line conjecture, which asserts that the nodal (zero) set of any eigenfunction associated with the second eigenvalue...

Nodal domain | Eigenfunction | Neumann boundary condition | Mathematics, general | Mathematics | Primary 35P05 | Laplacian | Secondary (35B05, 35J05, 58J50) | MATHEMATICS | PARTITIONS | FIXED MEMBRANE PROBLEM | 2ND EIGENFUNCTION | DOMAINS

Nodal domain | Eigenfunction | Neumann boundary condition | Mathematics, general | Mathematics | Primary 35P05 | Laplacian | Secondary (35B05, 35J05, 58J50) | MATHEMATICS | PARTITIONS | FIXED MEMBRANE PROBLEM | 2ND EIGENFUNCTION | DOMAINS

Journal Article

Integral Equations and Operator Theory, ISSN 0378-620X, 10/2018, Volume 90, Issue 5, pp. 1 - 32

... Subject Classiﬁcation. Primary 47A10, 47A60, Secondary 35Q61, 35J05. Keywords. Helmholtz equation, Maxwell’s equations, Electromagnetic waveguide, Acoustic waveguide...

Electromagnetic waveguide | Analysis | Primary 47A10 | Maxwell’s equations | Helmholtz equation | Mathematics | Secondary 35Q61 | 35J05 | Acoustic waveguide | 47A60 | Functional calculus | MATHEMATICS | Maxwell's equations | Waveguides | Electromagnetism | Matematik

Electromagnetic waveguide | Analysis | Primary 47A10 | Maxwell’s equations | Helmholtz equation | Mathematics | Secondary 35Q61 | 35J05 | Acoustic waveguide | 47A60 | Functional calculus | MATHEMATICS | Maxwell's equations | Waveguides | Electromagnetism | Matematik

Journal Article

Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 07/2016, Volume 439, Issue 1, pp. 347 - 363

We study the existence of nonnegative solutions (and ground states) to nonlinear Schrödinger equations in RN with radial potentials and super-linear or...

Unbounded or decaying potentials | Nonlinear Schrödinger equation | Sum of weighted Lebesgue spaces | Ground states | EXISTENCE | INFINITY | MATHEMATICS | MATHEMATICS, APPLIED | R-N | GROUND-STATE | LINEAR ELLIPTIC-EQUATIONS | V(INFINITY)=0 | EMBEDDINGS

Unbounded or decaying potentials | Nonlinear Schrödinger equation | Sum of weighted Lebesgue spaces | Ground states | EXISTENCE | INFINITY | MATHEMATICS | MATHEMATICS, APPLIED | R-N | GROUND-STATE | LINEAR ELLIPTIC-EQUATIONS | V(INFINITY)=0 | EMBEDDINGS

Journal Article

Integral Equations and Operator Theory, ISSN 0378-620X, 7/2013, Volume 76, Issue 3, pp. 381 - 401

... are given. Mathematics Subject Classiﬁcation (2010). Primary 34B45; Secondary 35J05, 34L15. Keywords. Differential operators on metric graphs, negative eigenvalues...

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

Calculus of Variations and Partial Differential Equations, ISSN 0944-2669, 10/2015, Volume 54, Issue 2, pp. 2239 - 2268

We study the nodal set of the Steklov eigenfunctions on the boundary of a smooth bounded domain in $$\mathbb {R}^n$$ R n - the eigenfunctions of the...

Systems Theory, Control | Calculus of Variations and Optimal Control; Optimization | Analysis | Theoretical, Mathematical and Computational Physics | Primary 35P99 | Mathematics | 35J05 | 47A75 | Secondary 35B05 | 35S05 | FRACTIONAL LAPLACIAN | EIGENVALUE | MATHEMATICS | CONSTANT MEAN-CURVATURE | MATHEMATICS, APPLIED | INEQUALITIES | EQUATIONS | BOUNDARY | CONFORMAL GEOMETRY | UNIQUE CONTINUATION | RIEMANNIAN-MANIFOLDS

Systems Theory, Control | Calculus of Variations and Optimal Control; Optimization | Analysis | Theoretical, Mathematical and Computational Physics | Primary 35P99 | Mathematics | 35J05 | 47A75 | Secondary 35B05 | 35S05 | FRACTIONAL LAPLACIAN | EIGENVALUE | MATHEMATICS | CONSTANT MEAN-CURVATURE | MATHEMATICS, APPLIED | INEQUALITIES | EQUATIONS | BOUNDARY | CONFORMAL GEOMETRY | UNIQUE CONTINUATION | RIEMANNIAN-MANIFOLDS

Journal Article

Zeitschrift für angewandte Mathematik und Physik, ISSN 0044-2275, 12/2018, Volume 69, Issue 6, pp. 1 - 30

The goal of this paper is to investigate the stability of the Helmholtz equation in the high-frequency regime with non-smooth and rapidly oscillating...

Secondary: 35J05 | Engineering | Mathematical Methods in Physics | 65N12 | 35B35 | Heterogeneous media | Stability estimates | Primary: 65N80 | Helmholtz equation | Theoretical and Applied Mechanics | High frequency | REAL AXIS | MATRIX | MATHEMATICS, APPLIED | CONVERGENCE ANALYSIS | DISCRETIZATIONS | MEDIA | ABSENCE | RESONANCES | SCATTERING | Mathematics - Numerical Analysis

Secondary: 35J05 | Engineering | Mathematical Methods in Physics | 65N12 | 35B35 | Heterogeneous media | Stability estimates | Primary: 65N80 | Helmholtz equation | Theoretical and Applied Mechanics | High frequency | REAL AXIS | MATRIX | MATHEMATICS, APPLIED | CONVERGENCE ANALYSIS | DISCRETIZATIONS | MEDIA | ABSENCE | RESONANCES | SCATTERING | Mathematics - Numerical Analysis

Journal Article

Calculus of Variations and Partial Differential Equations, ISSN 0944-2669, 9/2015, Volume 54, Issue 1, pp. 1061 - 1090

Given two measurable functions $$V(r )\ge 0$$ V ( r ) ≥ 0 and $$K(r)> 0$$ K ( r ) > 0 , $$r>0$$ r > 0 , we define the weighted spaces $$\begin{aligned}...

35J20 | 46E35 | Systems Theory, Control | Calculus of Variations and Optimal Control; Optimization | 35J60 | Analysis | Theoretical, Mathematical and Computational Physics | 46E30 | Mathematics | 35J05 | MATHEMATICS | ELLIPTIC PROBLEMS | MATHEMATICS, APPLIED | NONLINEAR SCHRODINGER-EQUATIONS | Origins | Infinity | Sobolev space | Mathematical analysis | Texts | Compatibility | Estimates | Calculus of variations

35J20 | 46E35 | Systems Theory, Control | Calculus of Variations and Optimal Control; Optimization | 35J60 | Analysis | Theoretical, Mathematical and Computational Physics | 46E30 | Mathematics | 35J05 | MATHEMATICS | ELLIPTIC PROBLEMS | MATHEMATICS, APPLIED | NONLINEAR SCHRODINGER-EQUATIONS | Origins | Infinity | Sobolev space | Mathematical analysis | Texts | Compatibility | Estimates | Calculus of variations

Journal Article

ADVANCES IN APPLIED CLIFFORD ALGEBRAS, ISSN 0188-7009, 11/2019, Volume 30, Issue 1

In this paper, we study the fundamental solution of natural powers of the n-parameter fractional Laplace and Dirac operators defined via Riemann-Liouville...

Poisson's equation | Fundamental solution | MATHEMATICS, APPLIED | EIGENFUNCTIONS | Laplace transform | PHYSICS, MATHEMATICAL | Fractional derivatives | Fractional Clifford analysis

Poisson's equation | Fundamental solution | MATHEMATICS, APPLIED | EIGENFUNCTIONS | Laplace transform | PHYSICS, MATHEMATICAL | Fractional derivatives | Fractional Clifford analysis

Journal Article

Potential Analysis, ISSN 0926-2601, 11/2018, Volume 49, Issue 4, pp. 527 - 554

Let n ≥ 3and Ω be a bounded Lipschitz domain in ℝn $\mathbb {R}^{n}$. Assume that the non-negative potential V belongs to the reverse Hölder class RHn(ℝn)...

Neumann problem | Lipschitz domain | Probability Theory and Stochastic Processes | Weak reverse Hölder inequality | Mathematics | Schrödinger equation | Primary: 35J25 | Geometry | Secondary: 35J05 | 42B25 | Potential Theory | Functional Analysis | Regularity problem | RIESZ TRANSFORMS | INEQUALITIES | SPACES | BOUNDARY-VALUE-PROBLEMS | POTENTIALS | Weak reverse Holder inequality | ELLIPTIC-OPERATORS | MATHEMATICS | Schrodinger equation | LAPLACES-EQUATION | DIRICHLET PROBLEM

Neumann problem | Lipschitz domain | Probability Theory and Stochastic Processes | Weak reverse Hölder inequality | Mathematics | Schrödinger equation | Primary: 35J25 | Geometry | Secondary: 35J05 | 42B25 | Potential Theory | Functional Analysis | Regularity problem | RIESZ TRANSFORMS | INEQUALITIES | SPACES | BOUNDARY-VALUE-PROBLEMS | POTENTIALS | Weak reverse Holder inequality | ELLIPTIC-OPERATORS | MATHEMATICS | Schrodinger equation | LAPLACES-EQUATION | DIRICHLET PROBLEM

Journal Article

Applied Mathematics & Optimization, ISSN 0095-4616, 2/2018, Volume 77, Issue 1, pp. 173 - 195

This paper describes different representations for solution operators of Laplacian boundary value problems on bounded regions in $${\mathbb R}^N, N \ge 2$$...

Systems Theory, Control | Laplacian boundary value problems | Theoretical, Mathematical and Computational Physics | Mathematics | Multipole expansions | 35J05 | Secondary 31B05 | Greens functions | Mathematical Methods in Physics | Steklov eigenfunctions | Calculus of Variations and Optimal Control; Optimization | 35P15 | Layer potentials | Numerical and Computational Physics, Simulation | Primary 35J08 | MATHEMATICS, APPLIED | SPACES | Dirichlet problem | Boundary value problems | Representations | Subspaces | Sobolev space

Systems Theory, Control | Laplacian boundary value problems | Theoretical, Mathematical and Computational Physics | Mathematics | Multipole expansions | 35J05 | Secondary 31B05 | Greens functions | Mathematical Methods in Physics | Steklov eigenfunctions | Calculus of Variations and Optimal Control; Optimization | 35P15 | Layer potentials | Numerical and Computational Physics, Simulation | Primary 35J08 | MATHEMATICS, APPLIED | SPACES | Dirichlet problem | Boundary value problems | Representations | Subspaces | Sobolev space

Journal Article

The Journal of Geometric Analysis, ISSN 1050-6926, 7/2018, Volume 28, Issue 3, pp. 2477 - 2502

.... Keywords Hamiltonian system · Kolmogorov operator · Quadratic potential · Geodesics · Heat kernel Mathematics Subject Classiﬁcation Primary 35J05 · Secondary 35F21...

Secondary 35F21 | Primary 35J05 | Heat kernel | Mathematics | Kolmogorov operator | Abstract Harmonic Analysis | Fourier Analysis | 15A24 | Convex and Discrete Geometry | Geodesics | Global Analysis and Analysis on Manifolds | Hamiltonian system | Differential Geometry | Dynamical Systems and Ergodic Theory | Quadratic potential | SUBELLIPTIC LAPLACIANS | OPTIONS | DIVERGENCE FORM | ULTRAPARABOLIC EQUATIONS | MATHEMATICS | DISCONTINUOUS COEFFICIENTS | REGULARITY | PHYSICS | COMPLEX HAMILTONIAN-MECHANICS | FUNDAMENTAL-SOLUTIONS | PARAMETRICES | Computer science | Analysis | Resveratrol

Secondary 35F21 | Primary 35J05 | Heat kernel | Mathematics | Kolmogorov operator | Abstract Harmonic Analysis | Fourier Analysis | 15A24 | Convex and Discrete Geometry | Geodesics | Global Analysis and Analysis on Manifolds | Hamiltonian system | Differential Geometry | Dynamical Systems and Ergodic Theory | Quadratic potential | SUBELLIPTIC LAPLACIANS | OPTIONS | DIVERGENCE FORM | ULTRAPARABOLIC EQUATIONS | MATHEMATICS | DISCONTINUOUS COEFFICIENTS | REGULARITY | PHYSICS | COMPLEX HAMILTONIAN-MECHANICS | FUNDAMENTAL-SOLUTIONS | PARAMETRICES | Computer science | Analysis | Resveratrol

Journal Article

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