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Annales de l'Institut Henri Poincare (C) Analyse Non Lineaire, ISSN 0294-1449, Volume 9, Issue 3, pp. 281 - 304
Let p=[formula presented], N ≧ 3 be the limiting Sobolev exponent and Ω ⊂ ℝ open bounded set. We show that for f ∈ H satisfying a suitable condition and f ≠ 0,... 
Semilinear elliptic equations | critical Sobolev exponent | MATHEMATICS, APPLIED | SEMILINEAR ELLIPTIC EQUATIONS | CRITICAL SOBOLEV EXPONENT | POSITIVE SOLUTIONS
Journal Article
Mediterranean Journal of Mathematics, ISSN 1660-5446, 4/2019, Volume 16, Issue 2, pp. 1 - 27
In this work, we have proved a Hardy–Littlewood–Sobolev inequality for variable exponents. After that, we use this inequality together with the variational... 
quasilinear elliptic equations | 35J62 | 35A15 | Variational methods | 35J60 | Choquard equation | Mathematics, general | Mathematics | nonlinear elliptic equations | EXISTENCE | MATHEMATICS, APPLIED | MULTIPLICITY | P(X)-LAPLACIAN EQUATIONS | POTENTIALS | CONVOLUTION | MATHEMATICS | R-N | REGULARITY | CRITICAL GROWTH | LEBESGUE SPACES | OPERATORS | Equality
Journal Article
Communications in Contemporary Mathematics, ISSN 0219-1997, 10/2015, Volume 17, Issue 5, pp. 1550005 - 1550001
Journal Article
Computers and Mathematics with Applications, ISSN 0898-1221, 09/2019, Volume 78, Issue 6, pp. 2063 - 2082
In this paper, we consider the following fractional Kirchhoff-type equation: a+b∫RN∫RN|u(x)−u(y)|2|x−y|N+2sdxdy(−Δ)su=Iα∗|u|2h,α∗|u|2h,α∗−2u,inRN,where N⩾3,... 
Moser iteration scheme | Fractional Kirchhoff-type equation | Hardy–Littlewood–Sobolev critical exponent | EXISTENCE | MATHEMATICS, APPLIED | MULTIPLICITY | POSITIVE SOLUTIONS | Hardy-Littlewood-Sobolev critical exponent
Journal Article
Journal of Differential Equations, ISSN 0022-0396, 09/2016, Volume 261, Issue 6, pp. 3061 - 3106
In this paper, we study the existence of ground state solutions for the nonlinear fractional Schrödinger–Poisson system with critical Sobolev... 
Fractional Schrödinger–Poisson system | Variational methods | Palais–Smale condition | Pohozaev identity | Palais-Smale condition | POSITIVE SOLUTIONS | CALCULUS | CONCENTRATION-COMPACTNESS PRINCIPLE | MAXWELL EQUATIONS | Fractional Schrodinger-Poisson system | GUIDE | LAPLACIAN | MATHEMATICS | R-N | CRITICAL GROWTH
Journal Article
Polymer, ISSN 0032-3861, 02/2016, Volume 84, pp. 275 - 285
A soluble polyimide (6FDA-TFDB) was synthesized and its properties in solution were investigated. The relationship between specific viscosity and concentration... 
Dipole–dipole interaction | Scaling exponent | Critical concentration | Soluble polyimide | Dipole-dipole interaction | ISOMERIZED POLYIMIDES | POLYMER SCIENCE | CHAIN CONFORMATION | BEHAVIOR | VISCOSITY | LOCAL RIGIDITY | DEPENDENCE | Polyimides | Solvents | Dilution | Exponents | Rheometers | Mathematical models | Deviation | Hydrogen bonding | Polyimide resins
Journal Article
by Su, Yu and Wang, Li and Han, Tao
Mathematical Methods in the Applied Sciences, ISSN 0170-4214, 09/2019, Volume 42, Issue 14, pp. 4815 - 4838
In this paper, we consider the following Schrödinger‐Poisson system: −Δu+λϕ|u|2α∗−2u=∫R3|u|2β∗|x−y|3−βdy|u|2β∗−2u,inR3,(−Δ)α2ϕ=Aα−1|u|2α∗,inR3, where... 
Hardy‐Littlewood‐Sobolev critical exponent | Schrödinger‐Poisson system | Kelvin transformation | Moser iteration | Hardy-Littlewood-Sobolev critical exponent | Schrödinger-Poisson system | EXISTENCE | Schrodinger-Poisson system | MATHEMATICS, APPLIED | EQUATIONS | GROUND-STATE SOLUTIONS | Perturbation methods
Journal Article
Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 2015, Volume 429, Issue 2, pp. 1153 - 1172
In this paper, we study the following nonlinear Kirchhoff-type equation where is nonnegative. By using the variational method, we obtain the existence of... 
Kirchhoff-type equation | Zero mass | Critical exponent | Variational methods | EXISTENCE | MATHEMATICS, APPLIED | STATES | MULTIPLICITY | CRITICAL NONLINEARITY | MATHEMATICS | CRITICAL GROWTH | R-3 | CRITICAL SOBOLEV EXPONENTS | ELLIPTIC-EQUATIONS
Journal Article
Nonlinear Analysis: Real World Applications, ISSN 1468-1218, 12/2016, Volume 32, pp. 198 - 212
Journal Article
Journal of Physics A: Mathematical and Theoretical, ISSN 1751-8113, 06/2017, Volume 50, Issue 26, p. 264003
We implement a scale-free version of the pivot algorithm and use it to sample pairs of three-dimensional self-avoiding walks, for the purpose of efficiently... 
pivot algorithm | self-avoiding walk | Monte Carlo | critical exponent
Journal Article
Mathematical Methods in the Applied Sciences, ISSN 0170-4214, 05/2019, Volume 42, Issue 7, pp. 2417 - 2430
In this paper, the existence and multiplicity of positive solutions is established for Schrödinger‐Poisson system of the form... 
Schrödinger‐poisson system | Nehari method | singularity | critical exponent | Schrödinger-poisson system | MATHEMATICS, APPLIED | BOUND-STATES | EQUATIONS | GROUND-STATE SOLUTIONS | Schrodinger-poisson system
Journal Article
Nonlinear Analysis, ISSN 0362-546X, 2009, Volume 70, Issue 6, pp. 2150 - 2164
In this paper we establish the existence of a positive solution of the Schrödinger–Poisson equations with a critical Sobolev exponent. The methods used here... 
Pohoz˘aev identity | Concentration–compactness principle | Critical growth | Variational methods | Pohoz ̌aev identity | Concentration-compactness principle | EXISTENCE | MATHEMATICS | MATHEMATICS, APPLIED | STATES | Pohozaev identity
Journal Article
Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 04/2017, Volume 448, Issue 2, pp. 1006 - 1041
Journal Article
Physical Review B - Condensed Matter and Materials Physics, ISSN 1098-0121, 06/2015, Volume 91, Issue 21
Relations between critical exponents, or scaling laws, at both continuous and discontinuous quantum phase transitions are derived and discussed. In general... 
PHYSICS, CONDENSED MATTER | PHYSICS, APPLIED | CRITICAL-BEHAVIOR | MATERIALS SCIENCE, MULTIDISCIPLINARY | CRITICAL-POINTS | Exponents | Phase transformations | Condensed matter | Asymptotic properties | Scaling laws | Inequalities | Ferromagnetism | Dynamical systems | Physics - Statistical Mechanics
Journal Article
Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 03/2020, Volume 483, Issue 2, p. 123647
We study multiplicity of positive solutions for a class of Schrödinger-Poisson system with singularity and critical exponent, and obtain two positive solutions... 
Schrödinger-Poisson systems | Critical exponent | Singular nonlinearity | Perturbation approach | EXISTENCE | MATHEMATICS, APPLIED | KLEIN-GORDON-MAXWELL | Schrodinger-Poisson systems | EQUATIONS | GROUND-STATE SOLUTIONS | MATHEMATICS | SOLITARY WAVES | BOUND-STATES | CONCAVE
Journal Article
Probability Theory and Related Fields, ISSN 0178-8051, 2013, Volume 160, Issue 1-2, pp. 1 - 13
We prove that for the Ising model defined on the plane at the average magnetization under an external magnetic field behaves exactly like The proof, which is... 
Mathematics Subject Classification: 82B20, 82B27, 60K35 | TRANSITION | STATISTICS & PROBABILITY | INEQUALITIES | MODEL | PERCOLATION | CRITICAL-POINT | Magnetization | Exponents | Lattices | Inequalities | Ising model | Texts | Percolation | Magnetic fields
Journal Article