Vitaly Moroz Home Page

Recent publications

P. D. Lamberti, V. Moroz, On the Phragmén-Lindelöf and the superposition principles for the p-Laplacian. arXiv:2405.16705
S. Ma, V. Moroz, Asymptotic profiles of ground state solutions for Choquard equations with a general local perturbation. arXiv:2405.02877
R. Molle, V. Moroz, G. Riey, Normalised solutions and limit profiles of the defocusing Gross-Pitaevskii-Poisson equation. arXiv:2308.04527
S. Ma, V. Moroz, Asymptotic profiles for Choquard equations with combined attractive nonlinearities: the locally critical case. Calc. Var. Partial Differential Equations 64, 127, (2025). [doi:10.1007/s00526-025-02986-8]
D. Greco, Y. Huang, Z. Liu, V. Moroz, Ground states of a nonlocal variational problem and Thomas-Fermi limit for the Choquard equation. J. Lond. Math. Soc. (2025) [doi:10.1112/jlms.70115]
S. Ma, V. Moroz, Asymptotic profiles for Choquard equations with combined attractive nonlinearities. J. Differential Equations 412 (2024), 613-689. [doi:10.1016/j.jde.2024.08.047]
V. Moroz, C. Muratov, Thomas-Fermi theory of out-of-plane charge screening in graphene. Proc. Royal Soc. Lond. Ser. A 480 (2024), no. 2294, 27pp. [doi:10.1098/rspa.2023.0570]
Y. Tang, Y. Huang, Z. Liu, V. Moroz, Symmetry breaking and multiple solutions for the Schrödinger-Poisson-Slater equation. Z. Angew. Math. Phys. 75, 114 (2024). [doi:10.1007/s00033-024-02261-4]
S. Ma, V. Moroz, Asymptotic profiles for a nonlinear Kirchhoff equation with combined powers nonlinearity. Nonlinear Analysis 239 (2024), 113423. [doi:10.1016/j.na.2023.113423]
M. Ghergu, Z. Liu, Y. Miyamoto, V. Moroz, Nonlinear Inequalities with Double Riesz Potentials. Potential Anal. 59 (2023), 97-112. [doi:10.1007/s11118-021-09962-9]
S. Ma, V. Moroz, Asymptotic profiles for a nonlinear Schrödinger equation with critical combined powers nonlinearity. Math. Z. 304 (2023), Paper No. 13, 26 pp. [doi:10.1007/s00209-023-03271-0]
F. Gao, V. Moroz, M. Yang, S. Zhao, Construction of infinitely many solutions for a critical Choquard equation via local Pohožaev identities. Calc. Var. Partial Differential Equations 61, 222 (2022). [doi:10.1007/s00526-022-02340-2]
Z. Liu, V. Moroz, Limit profiles for singularly perturbed Choquard equations with local repulsion. Calc. Var. Partial Differential Equations 61, 160 (2022). [doi:10.1007/s00526-022-02255-y]
Z. Liu, V. Moroz, Asymptotic profile of ground states for the Schrödinger-Poisson-Slater equation. Nonlinear Analysis 218 (2022), 112778. [doi:10.1016/j.na.2021.112778]
M. Ghergu, Y. Miyamoto, V. Moroz, Polyharmonic inequalities with nonlocal terms. J. Differential Equations 296 (2021), 799–821. [doi:10.1016/j.jde.2021.06.019]
F. Gao, H. Liu, V. Moroz, M. Yang, High energy positive solutions for a coupled Hartree system with Hardy-Littlewood-Sobolev critical exponents. J. Differential Equations 287 (2021), 329–375. [doi:10.1016/j.jde.2021.03.051]
Y. Kabeya, V. Moroz, Gelfand problem on a large spherical cap. Journal of Elliptic and Parabolic Equations 7 (2021), 1-23. [doi:10.1007/s41808-020-00091-9]
P. V. Gordon, V. Moroz, F. Nazarov, Gelfand-type problem for turbulent jets. J. Differential Equations 269 (2020), 5959-5996. [doi:10.1016/j.jde.2020.04.026]
M. Alyobi, C. Barnett, C. Muratov, V. Moroz, R. Cobley, The voltage-dependent manipulation of few-layer graphene with a scanning tunneling microscopy tip Carbon 163 (2020), 379-384. [doi:10.1016/10.1016/j.carbon.2020.03.046]
W. Albalawi, C. Mercuri, V. Moroz, Groundstate asymptotics for a class of singularly perturbed p-Laplacian problems in R^N. Annali di Matematica Pura ed Applicata 199 (2020), 23-63. [doi:10.1007/s10231-019-00865-6]
J. Bellazzini, M. Ghimenti, C. Mercuri, V. Moroz, J. Van Schaftingen, Sharp Gagliardo-Nirenberg inequalities in fractional Coulomb-Sobolev spaces. Trans. Amer. Math. Soc. 370 (2018), 8285-8310. [doi:10.1090/tran/7426]
M. Marcus, V. Moroz, Moderate solutions of semilinear elliptic equations with Hardy potential under minimal restrictions on the potential. Ann. Sc. Norm. Super. Pisa Cl. Sci. (5) 18 (2018), 39-64. [doi:10.2422/2036-2145.201604_002]
C. Bandle, M. Marcus, V. Moroz, Boundary singularities of solutions of semilinear elliptic equations in the half-space with a Hardy potential. Israel J. Math. 222 (2017), 487-514. [doi:10.1007/s11856-017-1598-4]
V. Moroz, J. Van Schaftingen, A guide to the Choquard equation. J. Fixed Point Theory Appl. 19 (2017), 773-813. [doi:10.1007/s11784-016-0373-1]
M. Ghimenti, V. Moroz, J. Van Schaftingen, Least action nodal solutions for the quadratic Choquard equation. Proc. Amer. Math. Soc. 145 (2017), 737-747. [doi:10.1090/proc/13247]
C. Mercuri, V. Moroz, J. Van Schaftingen, Groundstates and radial solutions to nonlinear Schrödinger-Poisson-Slater equations at the critical frequency. Calc. Var. Partial Differential Equations 55 (2016), Paper No. 146, 58 pp. [doi:10.1007/s00526-016-1079-3]
J. Lu, V. Moroz, C. Muratov, Orbital-free density functional theory of out-of-plane charge screening in graphene. J. Nonlinear Sci. 25 (2015), 1391-1430. [doi:10.1007/s00332-015-9259-4]
V. Moroz, J. Van Schaftingen, Groundstates of nonlinear Choquard equations: Hardy-Littlewood-Sobolev critical exponent. Commun. Contemp. Math. 17, 1550005 (2015). [doi:10.1142/S0219199715500054]
V. Moroz, J. Van Schaftingen, Existence of groundstates for a class of nonlinear Choquard equations. Trans. Amer. Math. Soc. 367 (2015), 6557-6579. [doi:10.1090/S0002-9947-2014-06289-2]
V. Moroz, J. Van Schaftingen, Semi-classical states for the Choquard equation. Calc. Var. Partial Differential Equations 52 (2015), 199-235. [doi:10.1007/s00526-014-0709-x]
V. Moroz, J. Van Schaftingen, Existence, stability and oscillation properties of slow decay positive solutions of supercritical elliptic equations with Hardy potential. Proc. Edinb. Math. Soc. 58 (2015), 255-271. [doi:10.1017/S0013091513000588]
V. Moroz, C. Muratov, Asymptotic properties of ground states of scalar field equations with a vanishing parameter. J. Eur. Math. Soc. 16 (2014), 1081-1109. [doi:10.4171/jems/455]
P. Gordon, V. Moroz, Gelfand type problem for two phase porous media. Proc. Royal Soc. Lond. Ser. A. 470 (2014), no. 2163, 17pp. [doi:10.1098/rspa.2013.0573]
V. Moroz, J. Van Schaftingen, Groundstates of nonlinear Choquard equations: existence, qualitative properties and decay asymptotics. J. Funct. Anal. 265 (2013), 153-184. [doi:10.1016/j.jfa.2013.04.007]
V. Moroz, J. Van Schaftingen, Nonexistence and optimal decay of supersolutions to Choquard equations in exterior domains. J. Differential Equations, 254 (2013), 3089-3145. [doi:10.1016/j.jde.2012.12.019]
V. Moroz, J. Van Schaftingen, Nonlocal Hardy type inequalities with optimal constants and remainder terms. Ann. Univ. Buchar. Math. Ser. 3 (LXI) (2012), 187-200.
C. Bandle, V. Moroz, W. Reichel, Large solutions to semilinear elliptic equations with Hardy potential and exponential nonlinearity. Around the Research of Vladimir Maz'ya II, Partial Differential Equations, 1-22, Int. Math. Ser. (N. Y.), 12, Springer, New York, 2010. [doi:10.1007/978-1-4419-1343-2_1]
V. Moroz, J. Van Schaftingen, Semiclassical stationary states for nonlinear Schrödinger equations with fast decaying potentials. Calc. Var. Partial Differential Equations, 37 (2010), 1-27. [doi:10.1007/s00526-009-0249-y]
V. Moroz, J. Van Schaftingen, Existence and concentration for nonlinear Schrödinger equations with fast decaying potentials, C. R. Math. Acad. Sci. Paris, Ser. I 347 (2009), 921-926. [doi:10.1016/j.crma.2009.05.009]
V. Moroz, Positive solutions to sublinear second-order divergence type elliptic equations in cone-like domains. J. Math. Anal. Appl. 352 (2009), 418-426. [doi:10.1016/j.jmaa.2008.05.062]
C. Bandle, V. Moroz, W. Reichel, 'Boundary blowup' type sub-solutions to semilinear elliptic equations with Hardy potential. J. London Math. Soc. (2) 77 (2008), 503-523. [doi:10.1112/jlms/jdm104]
V. Liskevich, S. Lyakhova, V. Moroz, Positive solutions to nonlinear p-Laplace equations with Hardy potential in exterior domains. J. Differential Equations 232 (2007), 212-252. [doi:10.1016/j.jde.2006.09.001]
V. Liskevich, S. Lyakhova, V. Moroz, Positive solutions to singular semilinear elliptic equations with critical potential on cone-like domains. Adv. Differential Equations 11 (2006), 361-398. [projecteuclid.org/euclid.ade/1355867701]
V. Liskevich, S. Lyakhova, V. Moroz, Positive solutions to semilinear elliptic equations with critical lower order terms. EQUADIFF 2003. Proceedings of the International Conference on Differential Equations. World Scientific, 2005. pp.549-557. [doi:10.1142/9789812702067_0091]
V. Kondratiev, V. Liskevich, V. Moroz, Z. Sobol, A critical phenomenon for sublinear elliptic equations in cone-like domains. Bull. Lond. Maths. Soc. 37 (2005), 585-591. [doi:10.1112/S0024609305004492]
V. Kondratiev, V. Liskevich, V. Moroz, Positive solutions to superlinear second-order divergence type elliptic equations in cone-like domains. Ann. Inst. H. Poincaré Anal. Non Linéaire 22 (2005), 25-43. [doi:10.1016/j.anihpc.2004.03.003]
V. Moroz, On the Morse critical groups for indefinite sublinear elliptic problems. Nonlinear Analysis 52 (2003), 1441-1453. [doi:10.1016/S0362-546X(02)00174-8]
F. Faraci, V. Moroz, Solutions of Hammerstein integral equations via a variational principle. J. Integral Equations Appl. 15 (2003), 385-402. [doi:10.1216/jiea/1181074983]
N. Jacob, V. Moroz, On the Log-Laplace equation for nonlocal operators generating sub-Markovian semigroups. Appl. Math. Optimization 45 (2002), 237-250. [doi:10.1007/s00245-001-0037-3]
N. Jacob, V. Moroz, On the semilinear Dirichlet Problem for a class of nonlocal operators generating Dirichlet forms. Recent Trends in Nonlinear Analysis, 191-204, Progr. Nonlinear Differential Equations Appl., 40 , Birkhauser, Basel, 2000. [doi:10.1007/978-3-0348-8411-2_18]
V. B. Moroz, P. P. Zabreiko, On the Hammerstein equations with natural growth conditions. Z. Anal. Anwendungen 18 (1999), 625-638. [doi:10.4171/ZAA/902]
V. Moroz, A. Vignoli, P. Zabreiko On the Three Critical Points Theorem. Topol. Methods Nonlinear Anal. 11 (1998), 103-113. [projecteuclid.org/euclid.tmna/1476842402]
V. Moroz, Solutions of superlinear at zero elliptic equations via Morse theory. Topol. Methods Nonlinear Anal. 10 (1997), 387-397. [projecteuclid.org/euclid.tmna/1476842213]
V. B. Moroz, P. P. Zabreiko, A Variant of the Mountain Pass Theorem and its Application to Hammerstein Integral Equations. Z. Anal. Anwendungen 15 (1996), 985-997. [doi:10.4171/ZAA/741]

Lecture Notes

Positivity principles and decay of solutions in semilinear elliptic problems. Lectures given at Online Mini-courses in Mathematical Analysis 2020, University of Padova, 14-17 September 2020.

Department of Mathematics
Swansea University
Swansea SA1 8EN
Wales, UK

v.moroz@swansea.ac.uk
+44 (0)1792 602763
Office: 322 CoFo