Alexandru Kristály

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  1. Balogh Z, Don S, Kristály A, Sharp weighted log-Sobolev inequalities: characterization of equality cases and applications [pdf]
  2. Kristály A, Mester Á, Mezei I. I, Anisotropic symmetrization and Sobolev inequalities on Finsler manifolds with nonnegative Ricci curvature [pdf]


  1. Costea N, Kristály A, Varga C, Variational and Monotonicity Methods in Nonsmooth Analysis, Frontiers in Mathematics, Birkhäuser/Springer, 2021. ISBN 978-3-030-81670-4.
  2. Kristály A, Rădulescu V, Varga C, Variational Principles in Mathematical Physics, Geometry, and Economics, Encyclopedia of Mathematics and its Applications, No. 136, Cambridge University Press, Cambridge, UK, 2010. ISBN-10: 0521117828 | ISBN-13: 9780521117821
  3. Kristály A, A Set-Valued Approach to Critical and Equilibrium Points, Casa Cartii de Stiinta, Cluj-Napoca, Romania, 2004. ISBN: 978-973-133-616-9.
  4. Kristály A, Varga C, An Introduction to Critical Point Theory for Non-smooth Functions, Casa Cartii de Stiinta, Cluj-Napoca, Romania, 2004. ISBN: 973-686-604-1.

Published or accepted papers:

  1. Kristály A, Lord Rayleigh’s Conjecture for Vibrating Clamped Plates in Positively Curved Spaces, GEOM FUNCT ANAL (GAFA), accepted, 2022 [pdf]
  2. Balogh Z, Kristály A, Sharp isoperimetric and Sobolev inequalities in spaces with nonnegative Ricci curvature, MATH ANNALEN, accepted, 2022, DOI: 10.1007/s00208-022-02380-1 [pdf]
  3. Kristály A, Zhao W, On the geometry of irreversible metric-measure spaces: Convergence, Stability and Analytic aspects, J MATH PURES APPL (Liouville Journal), 158 (2022), 216-292 [pdf]
  4. Kristály A, Shen Z, Yuan L, Zhao W, Nonlinear spectrums of Finsler manifolds, MATH. Z., 300 (2022), 81-123 [pdf]
  5. Farkas C, Kristály A, Mester Á, Compact Sobolev embeddings on non-compact manifolds via orbit expansions of isometry groups, CALCULUS OF VARIATIONS AND PDE, (2021) 60:128 [pdf]
  6. Kajántó S, Kristály A, Unexpected Behaviour of Flag and S-Curvatures on the Interpolated Poincaré Metric, J. GEOM. ANAL., 31 (2021), 10246–10262 [pdf] 
  7. Balogh Z, Gutiérrez E C, Kristály A, Sobolev inequalities with jointly concave weights on convex conesPROC. LOND. MATH. SOC., 122 (2021), no. 4, 537-568. [pdf]
  8. Kristály A, New features of the first eigenvalue on negatively curved spacesADV. CALC. VAR., accepted, DOI: [pdf]
  9. Huang L, Kristály A, Zhao W, Sharp uncertainty principles on general Finsler manifolds, TRANS. AMER. MATH. SOC., 373 (2020), no. 11, 8127–8161. [pdf]
  10. Kristály A, Fundamental tones of clamped plates in nonpositively curved spaces, ADV. MATH., 367 (2020), 107113, p. 39. [pdf]
  11. Kristály A,  Nodal solutions for the fractional Yamabe problem on Heisenberg groups, PROC. ROY. SOC. EDINBURGH SECT. A, 150 (2020), no. 2, 771–788. [pdf]
  12. Kristály A, Mezei I. I, Szilák K, Differential inclusions involving oscillatory terms, NONLINEAR ANALYSIS, 197 (2020), 111834, p. 21. [pdf]
  13. Balogh Z, Kristály A, Sipos K, Jacobian determinant inequality on corank 1 Carnot groups with applications, J. FUNCT. ANAL., 277 (2019), no. 12,  108293, p. 36. [pdf]
  14. Kristály A, New geometric aspects of Moser-Trudinger inequalities on Riemannian manifolds: the non-compact case, J. FUNCT. ANAL., 276 (2019), no. 8, 2359-2396. [pdf]
  15. Kristály A, Szakál A, Interpolation between Brezis-Vázquez and Poincaré inequalities on nonnegatively curved spaces: sharpness and rigidities,  J. DIFFERENTIAL EQUATIONS, 266 (2019), no. 10, 6621-6646. [pdf]
  16. Balogh Z, Kristály A, Equality in Borell-Brascamp-Lieb inequalities on curved spaces, ADV. MATH., 339 (2018), 453-494 [pdf]
  17. Balogh Z, Kristály A, Sipos K, Geometric inequalities on Heisenberg groupsCALCULUS OF VARIATIONS AND PDE, (2018) 57:61, 1-41. [pdf]
  18. Kristály A, Poincaré’s lemma on some non-Euclidean structuresCHINESE ANNALS OF MATHEMATICS, SERIES B (Special issue in honor of P. G. Ciarlet),  39 (2018), no. 2,  297–314[pdf]
  19. Barbosa E, Kristály A, Second-order Sobolev inequalities on Riemannian manifolds with nonnegative Ricci curvatureBULL. LONDON MATH. SOC., 50 (2018), no. 1, 35-45. [pdf]
  20. Faraci F, Farkas C, Kristály AMultipolar Hardy inequalities on Riemannian manifolds, ESAIM: CONTROL OPTIM. AND CALC. OF VARIATIONS,  24 (2018), no. 2, 551–567. [pdf]
  21. Kristály A, Sharp uncertainty principles on Riemannian manifolds: the influence of curvature,  J MATH PURES APPL  (Liouville Journal), 119 (2018), 326–346 [pdf]
  22. Kristály A, Metric measure spaces supporting Gagliardo-Nirenberg inequalities: volume non-collapsing and rigidities, CALCULUS OF VARIATIONS AND PDE 55 (2016), no. 5, Art. 112, 27 pp. [pdf]
  23. Farkas C, Kristály A, Schrödinger-Maxwell systems on non-compact Riemannian manifolds, NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS, 31 (2016), 473-491. [pdf]
  24. Kristály A, Repovš D, Quantitative Rellich inequalities on Finsler-Hadamard manifolds, COMMUN. CONTEMP. MATH.,18 (2016), no. 6, 1650020, 17 pp. [pdf]
  25. Balogh Z, Kristály A, Sipos K, Geodesic interpolation inequalities on Heisenberg groups, C. R. MATH. ACAD. SCI. PARIS 354 (2016), no. 9, 916–919. [pdf]
  26. Kristály A, Li C, López-Acedo G, Nicolae A, What do`convexities’ imply on Hadamard manifolds?, J. OPTIM. THEORY APPL. 170 (2016), no. 3, 1068–1074. [pdf]
  27. Kristály AA Sharp Sobolev Interpolation Inequality on Finsler ManifoldsJ. GEOM. ANAL. 25 (2015), no. 4, 2226–2240. [pdf]
  28. Farkas C, Kristály A, Varga CSingular Poisson equations on Finsler–Hadamard manifolds, CALCULUS OF VARIATIONS AND PDE 54 (2015), no. 2, 1219–1241. [pdf]
  29. Balogh Z, Calogero A, Kristály ASharp comparison and maximum principles via horizontal normal mapping in the Heisenberg group, J. FUNCT. ANAL. 269 (2015), no. 9, 2669–2708. [pdf]
  30. Kristály A, Rudas I J, Elliptic problems on the ball endowed with Funk-type metrics, NONLINEAR ANAL. 119 (2015), 199–208. [pdf]
  31. Kristály ASharp Morrey-Sobolev inequalities on complete Riemannian manifolds, POTENTIAL ANAL. 42 (2015), no. 1, 141–154. [pdf]
  32. Kristály A,  Nash-type equilibria on Riemannian manifolds: a variational approachJ MATH PURES APPL  (Liouville Journal), (9) 101 (2014), no. 5, 660–688 [pdf]
  33. Kristály A, Ohta S, Caffarelli-Kohn-Nirenberg inequality on metric measure spaces with applicationsMATH ANNALEN, 357:(2) 711-726 (2013). [pdf]
  34. Balogh Z, Kristály A, Lions-type compactness and Rubik actions on the Heisenberg group, CALCULUS OF VARIATIONS AND PDE, 48:(1-2) 89-109 (2013). [pdf]
  35. Kristály A, Repovš D, Metric projections versus non-positive curvature, DIFF GEOM APPL 31(5) 602-610 (2013). [pdf]
  36. Kristály A, Repovs D, On the Schrödinger–Maxwell system involving sublinear terms, NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS, 13:(1), 213-223 (2012). [pdf]
  37. Kristály ABifurcations effects in sublinear elliptic problems on compact Riemannian manifolds, J MATH ANAL APPL 385:(1) 179–184 (2012). [pdf]
  38. Faraci F,  Kristály AThree non-zero solutions for a nonlinear eigenvalue problem, J MATH ANAL APPL 394 (2012), no. 1, 225–230. [pdf]
  39.  Faraci F, Iannizzotto A, Kristály ALow-dimensional compact embeddings of symmetric Sobolev spaces with applications, P ROY SOC EDINB – SECTION A 141:(2) 383–395 (2011). [pdf]
  40. Kristály A, Repovs D, Multiple solutions for a Neumann system involving subquadratic nonlinearities, NONLINEAR ANALYSIS-TMA, 74:(6)  2127–2132 (2011). [pdf]
  41. Kristály A, Mihăilescu M, Rădulescu R, Tersian S, Spectral estimates for a nonhomogeneous difference problem, COMMUN CONTEMP MATH  12:(6) 1015–1029 (2010). [pdf]
  42. Kristály ALocation of Nash equilibria: a Riemannian geometrical approach, PROC AMER MATH SOC 138:(5) 1803-1810 (2010). [pdf]
  43. Kristály AOn a new class of elliptic systems with nonlinearities of arbitrary growthJ DIFFERENTIAL EQUATIONS, 249:(8) 1917–1928 (2010). [pdf]
  44. Kristály A, Morosanu Gh, New competition phenomena in Dirichlet problemsJ MATH PURES APPL  (Liouville Journal), 94:(6) 555-570 (2010). [pdf]
  45. Kristály A, Marzantowicz W, Varga Cs, A non-smooth three critical points theorem with applications in differential inclusions, J GLOBAL OPTIM 46:(1) 49-62 (2010). [pdf]
  46. Kristály A, Papageorgiou NS, Multiple nontrivial solutions for Neumann problems involving the p-Laplacian: a Morse theoretical approach, ADV NONLINEAR STUD 10:(1), 83-107 (2010). [pdf]
  47. Kristály A, Papageorgiou NS, Varga Cs, Multiple solutions for a class of Neumann elliptic problems on compact Riemannian manifolds with boundary, CANAD MATH BULL 53:(4)  674–683 (2010).
  48. Kristály A, Asymptotically critical problems on higher-dimensional spheres, DISCRETE CONT DYN SYSTEMS 23: (3) 919-935 (2009). [pdf]
  49. Kristály A, Varga C, Multiple solutions for a degenerate elliptic equation involving sublinear terms at infinity, J MATH ANAL APPL 352: (1) 139-148 (2009). [pdf]
  50. Kristály A, Papageorgiou NS, Multiplicity theorems for semilinear elliptic problems depending on a parameter, P EDINBURGH MATH SOC 52: (1) 171-180 (2009). [pdf]
  51. Kristály A, Radulescu V, Sublinear eigenvalue problems on compact Riemannian manifolds with applications in Emden-Fowler equationsSTUD MATH 191: (3) 237-246 (2009). [pdf]
  52. Kristály A, Mihailescu M, Radulescu V, Two nontrivial solutions for a non-homogeneous Neumann problem: an Orlitz-Sobolev space setting, P ROY SOC EDINB – SECTION A 139: 367-379 (2009). [pdf]
  53. Filippakis M, Kristály A, Papageorgiou NS, Existence of five nonzero solutions with exact sign for a p-Laplacian equation, DISCRETE CONT DYN SYSTEMS 24: (2) 405-440 (2009). [pdf]
  54. Kristály ADetection of arbitrarily many solutions for perturbed elliptic problems involving oscillatory terms, J DIFFERENTIAL EQUATIONS 245: (12) 3849-3868 (2008). [pdf]
  55. Kristály A, Lisei H, Varga C, Multiple solutions for p-Laplacian type equations, NONLINEAR ANALYSIS-TMA 68: (5) 1375-1381 (2008). [pdf]
  56.   Kristály A, Marzantowicz W, Multiplicity of symmetrically distinct sequences of solutions for a quasilinear problem in RN, NODEA- NONLINEAR DIFF EQUATIONS APPL 15: (1-2) 209-216 (2008). [pdf]
  57. Kristály A, Morosanu G, Roth A, Optimal placement of a deposit between markets:Riemann-Finsler geometrical approach, J OPTIM THEORY APPL 139: (2) 263-276 (2008). [pdf]
  58. Kristály APerturbed Neumann problems with many solutions, NUMER FUNC ANAL OPT 29: (8/9) 1114-1127 (2008). [pdf]
  59. Kristály AA double eigenvalue problem for Schrodinger equations involving sublinear nonlinearities at infinity, ELECTR J DIFFER EQUAT 42: (42) 1-11 (2007).
  60. Kristály A, Varga C, Varga V, A nonsmooth principle of symmetric criticality and variational-hemivariational inequalitiesJ MATH ANAL APPL 325: (2) 975-986 (2007). [pdf]
  61. Kristály A, Varga C, Multiple solutions for elliptic problems with singular and sublinear potentials, P AMER MATH SOC 135: (7) 2121-2126 (2007). [pdf]
  62. Kristály AMultiple solutions of a sublinear Schrodinger equation, NODEA-NONLINEAR DIFF EQUATIONS APPL 14: (3-4) 291-302 (2007). [pdf]
  63. Kristály A, Motreanu D, Nonsmooth Neumann-type problems involving the p-Laplacian, NUMER FUNC ANAL OPT 28: (11-12) 1309-1326 (2007). [pdf]
  64. Kristály A, Faraci F, On an open question of Ricceri concerning a Neumann problem, GLASGOW MATH J 49: (2) 189-195 (2007). [pdf]
  65. Kristály A, Faraci F, One-dimensional scalar field equations involving an oscillatory nonlinear term, DISCRETE CONT DYN SYSTEMS 18: (1) 107-120 (2007). [pdf]
  66. Kristály A, Morosanu G, Tersian S, Quasilinear elliptic problems in involving oscillatory nonlinearities, J DIFFERENTIAL EQUATIONS 235: (2) 366-375 (2007). [pdf]
  67. Kozma L, Kristály AMetric characterization of Berwald spaces of non-positive flag curvature, J GEOMETRY PHYSICS 56: 1257-1270 (2006). [pdf]
  68. Kristály AExistence of nonzero weak solutions for a class of elliptic variational inclusions systems in RN, NONLINEAR ANALYSIS-TMA 65: (8) 1578-1594 (2006). [pdf]
  69. Kristály AInfinitely many solutions for a differential inclusion problem in RN, J DIFFERENTIAL EQUATIONS 220: (2) 511-530 (2006). [pdf]
  70. Kristály A, Motreanu V, Varga C, A minimax principle with general Palais-Smale conditions, COMMUN APPL ANAL 9: (2) 285-299 (2005). [pdf]
  71. Kristály A, Varga C, Varga V, An eigenvalue problem for hemivariational inequalities with combined nonlinearities on an infinite strip, NONLINEAR ANALYSIS-TMA 63: (2) 260-277 (2005). [pdf]
  72. Kristály AExistence of two nontrivial solutions for a class of quasilinear elliptic variational systems on strip-like domain, P EDINBURGH MATH SOC 48: (2) 465-477 (2005). [pdf]
  73. Kristály AInfinitely many radial and non-radial solutions for a class of hemivariational inequalities, ROCKY MT J MATH 35: (4) 1173-1190 (2005). [pdf]
  74. Kristály AMultiplicity results for an eigenvalue problem for hemi-variational inequalities in strip-like domainsSET-VALUED ANAL 13: (1) 85-103 (2005). [pdf]
  75. Kristály A, Varga C, On a class of a quasilinear elliptic problem in RN, MATH NACHR 275: (15) 1756-1765 (2005). [pdf]
  76. Kozma L, Kristály A, Varga C, Dispersing of geodesics in Berwald spaces of nonpositive flag, HOUSTON J MATH 30: (2) 403-420 (2004).  [pdf]
  77. Kristály A, Varga C, Set-valued versions of Ky Fan’s inequality with application to variational inclusion theory, J MATH ANAL APPL 282: (1) 8-20 (2003). [pdf]

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