Nonautonomous Dynamical Systems, ISSN 2353-0626, 12/2019, Volume 6, Issue 1, pp. 99 - 107

In this paper, we study the existence of a non-trivial weak solution to the following singular elliptic equations with subcritical nonlinearities: where Ω ⊂ℝ...

positive solution | Primary 35J05, 35J25 | Hardy potential | Secondary 46E35 | Nonlinear elliptic equation | nonlinear elliptic equation | hardy potential | secondary 46e35 | primary 35j05, 35j25

positive solution | Primary 35J05, 35J25 | Hardy potential | Secondary 46E35 | Nonlinear elliptic equation | nonlinear elliptic equation | hardy potential | secondary 46e35 | primary 35j05, 35j25

Journal Article

Complex Variables and Elliptic Equations, ISSN 1747-6933, 11/2019, Volume 64, Issue 11, pp. 1844 - 1853

We consider the semilinear elliptic problem: where is an open bounded subset, Under assumptions small we show that there exists a solution to this problem. The...

positive solution | Hardy potential | Secondary 46E35 | Nonlinear elliptic equation | Primary 35J05 | EXISTENCE | MATHEMATICS | EQUATIONS

positive solution | Hardy potential | Secondary 46E35 | Nonlinear elliptic equation | Primary 35J05 | EXISTENCE | MATHEMATICS | EQUATIONS

Journal Article

Journal of Fourier Analysis and Applications, ISSN 1069-5869, 10/2019, Volume 25, Issue 5, pp. 2356 - 2418

In this work we extend the theory of the classical Hardy space $$H^1$$ H 1 to the rational Dunkl setting. Specifically, let $$\Delta $$ Δ be the Dunkl...

Hardy spaces | Secondary 33C52 | Mathematics | Cauchy–Riemann equations | 35J05 | Maximal operators | Abstract Harmonic Analysis | Riesz transforms | Mathematical Methods in Physics | 42B35 | Fourier Analysis | 42B25 | Signal,Image and Speech Processing | Primary 42B30 | 35K08 | Approximations and Expansions | 42B37 | Rational Dunkl theory | Partial Differential Equations

Hardy spaces | Secondary 33C52 | Mathematics | Cauchy–Riemann equations | 35J05 | Maximal operators | Abstract Harmonic Analysis | Riesz transforms | Mathematical Methods in Physics | 42B35 | Fourier Analysis | 42B25 | Signal,Image and Speech Processing | Primary 42B30 | 35K08 | Approximations and Expansions | 42B37 | Rational Dunkl theory | Partial Differential Equations

Journal Article

Advances in Nonlinear Analysis, ISSN 2191-9496, 10/2019, Volume 9, Issue 1, pp. 1026 - 1045

This paper presents local and global bifurcation results for radially symmetric solutions of the cubic Helmholtz system It is shown that every point along any...

Primary: 35J05 | bifurcation | Nonlinear Helmholtz sytem | Secondary: 35B32 | MATHEMATICS | MATHEMATICS, APPLIED | nonlinear helmholtz sytem | secondary: 35b32 | primary: 35j05

Primary: 35J05 | bifurcation | Nonlinear Helmholtz sytem | Secondary: 35B32 | MATHEMATICS | MATHEMATICS, APPLIED | nonlinear helmholtz sytem | secondary: 35b32 | primary: 35j05

Journal Article

Advances in applied Clifford algebras, ISSN 1661-4909, 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

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

Archiv der Mathematik, ISSN 1420-8938, 2018, 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

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

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

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

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

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

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

Annali di Matematica Pura ed Applicata (1923 -), ISSN 0373-3114, 12/2017, Volume 196, Issue 6, pp. 2023 - 2042

This paper studies for large frequency number $$k>0$$ k > 0 the existence and multiplicity of solutions of the semilinear problem $$\begin{aligned} -\varDelta...

Primary 35J20 | Lusternik–Schnirelmann category | Concentration of solutions | Nonlinear Helmholtz equation | Secondary 35J05 | Mathematics, general | Mathematics | Dual variational method | SCHRODINGER-EQUATIONS | MATHEMATICS | ELLIPTIC PROBLEMS | MATHEMATICS, APPLIED | POSITIVE BOUND-STATES | COMPETING POTENTIAL FUNCTIONS | Lusternik-Schnirelmann category | GENERAL NONLINEARITY | Cytokinins

Primary 35J20 | Lusternik–Schnirelmann category | Concentration of solutions | Nonlinear Helmholtz equation | Secondary 35J05 | Mathematics, general | Mathematics | Dual variational method | SCHRODINGER-EQUATIONS | MATHEMATICS | ELLIPTIC PROBLEMS | MATHEMATICS, APPLIED | POSITIVE BOUND-STATES | COMPETING POTENTIAL FUNCTIONS | Lusternik-Schnirelmann category | GENERAL NONLINEARITY | Cytokinins

Journal Article

Complex analysis and operator theory, ISSN 1661-8262, 2017, Volume 12, Issue 8, pp. 1991 - 2001

... · Lipschitz continuity Mathematics Subject Classiﬁcation Primary 30C62 · 30L10 · 31A30 · 31B30; Secondary 26A16 · 33C05 · 35J05 · 30C20 1 Introduction and Main Results...

30C20 | Primary 30C62 | 31B30 | 31A30 | Distance ratio metric | Mathematics | 35J05 | 30L10 | 33C05 | Harmonic and polyharmonic mappings | Lipschitz continuity | Secondary 26A16 | Operator Theory | Quasiconformal mappings | Analysis | Mathematics, general | MATHEMATICS, APPLIED | HALF-PLANE | UNIT DISK | REGULAR-MAPPINGS | MATHEMATICS | BOUNDARY CORRESPONDENCE | HARMONIC-MAPPINGS | POLYHARMONIC FUNCTIONS | JORDAN DOMAINS

30C20 | Primary 30C62 | 31B30 | 31A30 | Distance ratio metric | Mathematics | 35J05 | 30L10 | 33C05 | Harmonic and polyharmonic mappings | Lipschitz continuity | Secondary 26A16 | Operator Theory | Quasiconformal mappings | Analysis | Mathematics, general | MATHEMATICS, APPLIED | HALF-PLANE | UNIT DISK | REGULAR-MAPPINGS | MATHEMATICS | BOUNDARY CORRESPONDENCE | HARMONIC-MAPPINGS | POLYHARMONIC FUNCTIONS | JORDAN DOMAINS

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

Applicable Analysis: Applied Analysis and Optimization, ISSN 0003-6811, 10/2017, Volume 96, Issue 14, pp. 2457 - 2473

In this paper, we study a class of degenerate elliptic operators with quadratic potentials by Hamiltonian formalism. Geodesics induced by the operators are...

quadratic potential | geodesics | degenerate elliptic operator | heat kernel | Hamiltonian system | Primary: 35J05 | Secondary: 35F21 | MATHEMATICS, APPLIED | INTEGRAL-EQUATIONS | RADIATIVE-TRANSFER | SOLIDS | TRANSPORT-EQUATION | PHYSICS | PHOTOELECTRONS | FUNDAMENTAL-SOLUTIONS | Kernels | Operators (mathematics) | Geodesy

quadratic potential | geodesics | degenerate elliptic operator | heat kernel | Hamiltonian system | Primary: 35J05 | Secondary: 35F21 | MATHEMATICS, APPLIED | INTEGRAL-EQUATIONS | RADIATIVE-TRANSFER | SOLIDS | TRANSPORT-EQUATION | PHYSICS | PHOTOELECTRONS | FUNDAMENTAL-SOLUTIONS | Kernels | Operators (mathematics) | Geodesy

Journal Article

Experimental Mathematics, ISSN 1058-6458, 10/2017, Volume 26, Issue 4, pp. 381 - 395

We study partitions of the two-dimensional flat torus into k domains, with b a real parameter in (0, 1] and k an integer. We look for partitions which minimize...

minimal partitions | shape optimization | Primary 49Q10 | Secondary 35J05 | finite difference method | Dirichlet-Laplacian eigenvalues | projected gradient algorithm | MATHEMATICS | EIGENVALUES | DOMAINS | Numerical Analysis | Mathematics | Spectral Theory

minimal partitions | shape optimization | Primary 49Q10 | Secondary 35J05 | finite difference method | Dirichlet-Laplacian eigenvalues | projected gradient algorithm | MATHEMATICS | EIGENVALUES | DOMAINS | Numerical Analysis | Mathematics | Spectral Theory

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

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