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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
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
Journal Article
Journal of Fourier Analysis and Applications, ISSN 1069-5869, 10/2019, Volume 25, Issue 5, pp. 2356 - 2418
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
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
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
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
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
Journal Article
The Journal of Geometric Analysis, ISSN 1050-6926, 7/2018, Volume 28, Issue 3, pp. 2477 - 2502
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
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
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
Journal Article
Annali di Matematica Pura ed Applicata (1923 -), ISSN 0373-3114, 12/2017, Volume 196, Issue 6, pp. 2023 - 2042
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
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
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
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
Journal Article
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