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Calculus of Variations and Partial Differential Equations, ISSN 0944-2669, 9/2015, Volume 54, Issue 1, pp. 1061 - 1090
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
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
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 $$\begin{aligned} {\left\{ \begin{array}{ll} -\Delta u=|x|^\alpha |u|^{p_\alpha... 
35J40 | Secondary 35J05 | Lyapunov–Schmidt reduction | Hénon-type equation | Mathematics, general | Mathematics | Primary 35J60 | Sign-changing bubble tower solutions | Information science
Journal Article
Archiv der Mathematik, ISSN 0003-889X, 3/2019, Volume 112, Issue 3, pp. 305 - 311
We show that the Faber–Krahn inequality implies Pólya’s conjecture for eigenvalues $$\lambda _{k}$$ λ k of the Dirichlet Laplacian in $$\mathbb {R}^n$$ R n up... 
Dirichlet Laplacian | Secondary 35J05 | Eigenvalues | Pólya’s conjecture | Mathematics, general | Mathematics | Faber–Krahn inequality | 35P20 | 35J25 | Primary 35P15
Journal Article
Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 11/2016, Volume 443, Issue 2, pp. 707 - 731
Mellin convolution equations acting in Bessel potential spaces are considered. The study is based upon two results. The first one concerns the interaction of... 
Operator algebras | Fixed singularities | Fourier convolutions | Bessel potential spaces | Symbol | Mellin convolutions | MATHEMATICS | MATHEMATICS, APPLIED | STABILITY | PSEUDODIFFERENTIAL-OPERATORS | INTEGRAL-OPERATORS | Algebra | Mathematics - Functional Analysis
Journal Article
Integral Equations and Operator Theory, ISSN 0378-620X, 10/2018, Volume 90, Issue 5, pp. 1 - 32
We study time-harmonic electromagnetic and acoustic waveguides, modeled by an infinite cylinder with a non-smooth cross section. We introduce an infinitesimal... 
Electromagnetic waveguide | Analysis | Primary 47A10 | Maxwell’s equations | Helmholtz equation | Mathematics | Secondary 35Q61 | 35J05 | Acoustic waveguide | 47A60 | Functional calculus | MATHEMATICS | Maxwell's equations | Waveguides | Electromagnetism | Matematik
Journal Article
Journal of Evolution Equations, ISSN 1424-3199, 6/2014, Volume 14, Issue 2, pp. 477 - 497
For a finite not necessarily compact metric graph, one considers the differential expression $${-\frac{d^2}{d x^2}}$$ - d 2 d x 2 on each edge. The boundary... 
47D06 | Secondary 35J05 | Analysis | Differential operators on metric graphs | 35K05 | Mathematics | Primary 34B45 | Quasi-contractive semigroups | Quasi-m-accretive Laplacians | MATHEMATICS | EIGENVALUES | MATHEMATICS, APPLIED
Journal Article
Nonlinear Differential Equations and Applications NoDEA, ISSN 1021-9722, 4/2018, Volume 25, Issue 2, pp. 1 - 26
This paper considers a pair of coupled nonlinear Helmholtz equations $$\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
Constructive Approximation, ISSN 0176-4276, 4/2017, Volume 45, Issue 2, pp. 243 - 271
This paper deals with an extremal problem for harmonic functions in the unit ball of $$\mathbf {R}^n$$ R n . We are concerned with the pointwise sharp... 
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
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
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
Calculus of Variations and Partial Differential Equations, ISSN 0944-2669, 10/2015, Volume 54, Issue 2, pp. 2239 - 2268
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, 8/2016, Volume 195, Issue 4, pp. 1333 - 1345
In a bounded domain $$\varOmega $$ Ω , we consider a positive solution of the problem $$\Delta u+f(u)=0$$ Δ u + f ( u ) = 0 in $$\varOmega $$ Ω , $$u=0$$ u = 0... 
Primary 35B06 | Secondary 35B35 | Stability | 35J61 | Method of moving planes | Mathematics | Serrin’s problem | 35J05 | 35B09 | Stationary surfaces | Overdetermined problems | Harnack’s inequality | Mathematics, general
Journal Article
Archiv der Mathematik, ISSN 0003-889X, 2/2015, Volume 104, Issue 2, pp. 177 - 187
This paper shows that the L p -Helmholtz decomposition is not necessary to establish the analyticity of the Stokes semigroup in C 0,σ , the L ∞-closure of the... 
Neumann problem | Weighted estimate | Secondary 35Q30 | Primary 35J05 | Helmholtz decomposition | Mathematics, general | Mathematics | 76D07 | Sector-like domain | ANALYTICITY | MATHEMATICS | OPERATOR | SPACES | INFINITE-LAYER
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
Journal Article
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