Nonlinear Partial Differential Equations
Variational and topological methods in nonlinear analysis
Conformal Geometry
Publications:
[44] G. Vaira, Blow-up phenomena for a boundary Yamabe problem with umbilic boundary,arXiv: 2508.10387.
[43] S. Caputo, G. Vaira, Infinitely many non-radial solutions to a critical Choquard equation, preprint arXiv:2507.15747
[42] F. Li, G. Vaira, J. Wei, Y. Wu, Construction of bubbling solutions of the Brezis-Nirenberg problem in general bounded domains (II): the dimension 6, preprint.
[41] A. Pistoia, G. M. Rago, G. Vaira, Multi-bubble solutions for the Brezis-Nirenberg problem in four dimensions, preprint arXiv:2505.24387.
[40] F. Li, G. Vaira, J. Wei, Y. Wu, Construction of bubbling solutions of the Brezis-Nirenberg problem in general bounded domains (I): the dimensions 4 and 5, Journal of the London Mathematical Society, 2025, 112(2), e70246.
[39] L. Battaglia, Y. Pu, G. Vaira, Infinitely many solutions for a boundary Yamabe problem, Nonlinear Differential Equations and Applications, 2025, 32(5), 94.
[38] S. Caputo, G. Vaira, Partially concentrating solutions for systems with Lotka-Volterra type interactions, preprint arXiv:2411.08428
[37] M. Musso, S. Rocci, G. Vaira, Nodal cluster solutions for the Brezis-Nirenberg problem in dimensions N\geq 7, Calculus of Variations and Partial Differential Equations, 2024, 63(5), 119.
[36] B. Pellacci, A. Pistoia, G. Vaira, G. Verzini, Partially concentrating standing waves for weakly coupled Schrödinger systems, Mathematische Annalen, 2024, 390(3), pp. 3691–3722.
[35] S.Cruz-Blàzquez, G. Vaira, Positive Blow-up Solutions for a Linearly Perturbed Boundary Yamabe Problem, Discrete and Continuous Dynamical Systems Series A, 2025, 45(8), pp. 2518--2539.
[34] S. Cruz-Blàzquez, A. Pistoia, G. Vaira, Clustering phenomena in low dimensions for a boundary Yamabe problem, in corso di stampa su Annali Scuola Normale Superiore di Pisa - Classe di Scienze, DOI: 10.2422/2036-2145.202309_002.
[33] H. Chen, A. Pistoia, G. Vaira, Segregated solutions for some non-linear Schrödinger systems with critical growth, Discrete and Continuous Dynamical Systems- Series A, 43 (1) (2023), 482--506.
[32] A. Pistoia, G. Vaira, Segregated solutions for nonlinear Schrödinger systems with weak interspecies forces, Communications in Partial Differential Equations 47 (2022), no. 11, 2146–2179.
[31] M. Kowalczyk, A. Pistoia, G. Vaira, Phase separating solutions for two component systems in general planar domains, Calculus of Variations and Partial Differential Equations 62 (2023), no. 5, Paper No. 142, 46 pp.
[30] A. Pistoia, G. Vaira, Nodal Solutions of the Brezis-Nirenberg Problem in Dimension 6, Analysis in Theory and Applications, 38 (2022), 1--25.
[29] A. L. Amadori, F. Gladiali, M. Grossi, G. Vaira, A complete scenario on nodal radial solutions to the Brezis Nirenberg problem in low dimensions,Nonlinearity, 34 (11) (2021), 8055--8093.
[28] B. Pellacci, A. Pistoia, G. Vaira, G. Verzini, Normalized concentrating solutions to nonlinear elliptic problems, Journal of Differential Equations, 275 (2021), 882--919.
[27] A. Pistoia, G. Vaira, Nondegeneracy of the bubble for the critical p-Laplace equation, Proceedings of the Royal Society of Edinburgh Section A: Mathematics, 151 (1) (2021) 151--168.
[26] P. Esposito, N. Ghoussoub, A. Pistoia, G. Vaira, Sign-changing solutions for critical equations with hardy potential, Analysis and PDE, 14 (2) (2021), 533--566.
[25] F. Oliva, B. Sciunzi, G. Vaira, Radial symmetry for a quasilinear elliptic equation with a critical Sobolev growth and Hardy potential, Journal des Mathematique Pures et Appliquees, 140 (2020), 89--109.
[24] M. Kowalczyk, A. Pistoia, G. Vaira, Maximal solution of the Liouville equation in doubly connected domains, Journal of Functional Analysis, 277 no. 9 (2019), 2997-3050.
[23] M. Kowalczyk, A. Pistoia, P. Rybka, G. Vaira, Free boundary problems arising in the theory of maximal solutions of equations with exponential nonlinearities, S\'eminaire L. Schwartz - EDP and applications, Expos\'e n. X, (2019), 1-12.
[22] A. Pistoia, G. Vaira, Clustering phenomena for linear perturbation of the Yamabe equation, Partial differential equations arising from physics and geometry, 311--331, London Math. Soc. Lecture Note Ser., 450, Cambridge Univ. Press, Cambridge, (2019)
[21] A. Iacopetti, G. Vaira, Sign-changing blowing-up solutions for the Brezis--Nirenberg problem in dimensions four and five, Annali Scuola Normale Superiore di Pisa - Classe di Scienze (5) Vol. XVIII (2018), 1--38.
[20] A. Azzollini, P. d'Avenia, G. Vaira, Generalized Schrodinger - Newton system in dimension N\geq 3; critical case, Journal of Mathematical Analysis and Applications, 449 (2017) no. 1, 531--552.
[19] F. Morabito, A. Pistoia, G. Vaira, Towering phenomena for linear perturbation of the Yamabe problem in a symmetric manifold, Potential Analysis, 47 (2017), no. 1, 53--102.
[18] C. D. Pagani, D. Pierotti, A. Pistoia, G. Vaira, Concentration along geodesics for a nonlinear Steklov problem arising in corrosion modelling, SIAM Journal on Mathematical Analysis, 48 (2016) no. 2, 1085--1108.
[17] M. del Pino, A. Pistoia, G. Vaira, Large mass boundary condensation patterns in the stationary Keller-Segel system, Journal of Differential Equations {\bf 261}, no. 6 (2016), 3414--3462.
[16] A. Iacopetti, G. Vaira, Sign-changing tower of bubbles for the Brezis-Nirenberg problem, Communications in Contemporary Mathematics 18 (2016) no. 1 155036 (53 pp.).
[15] J. Dàvila, A. Pistoia, G. Vaira, Bubbling solutions for supercritical problems on manifolds, Journal des Mathematique Pures et Appliquees Vol. 103 (2015), 1410 - 1440.
[14] A. Pistoia, G. Vaira, From periodic ODE's to supercritical PDE's, Nonlinear Analysis, Theory, Methods and Applications, Vol. 119 (2015), 330 - 340.
[13] G. Vaira, A new kind of blowing -up solutions for the Brezis-Nirenberg problem, Calculus of Variations and PDEs, Vol. 52 (2015) no. 1--2, 389--422.
[12] A. Pistoia, G. Vaira, Steady states with unbounded mass of the Keller-Segel system, Proceedings of the Royal Society of Edinburgh, Vol. 145A (2015) no. 1 203--222.
[11] I. Ianni and G. Vaira, Non-radial sign-changing solution for the Schr\"{o}dinger-Poisson problem in the semiclassical limit, NoDea, Nonlinear Differential Equations and Applications, Vol. 22 no. 4 (2015) 741 – 776.
[10] A.Pistoia, G. Vaira, On the Stability for Paneitz type equations, International Mathematics Research Notices, Vol. 2013 (2013), 3133--3158.
[9] G. Vaira, Existence of bound states for Schr\"odinger-Newton type systems, Advanced Nonlinear Studies, Vol. 13 (2013) no. 2, 495--516.
[8] G. Vaira, Ground states for a Schr\"odinger-Poisson type systems, Ricerche di Matematica Vol. 60 (2011) no. 2, 263--297.
[7] P. d'Avenia, A. Pomponio, G. Vaira, Infinitely many positive solutions for a Schrödinger-Poisson system, Applied Mathematics Letters 24 (2011), no. 5, 661--664.
[6] P. d'Avenia, A. Pomponio, G. Vaira, Infinitely many positive solutions for a Schrödinger-Poisson system, Nonlinear Analysis, Theory, Methods and Applications 74 (2011), no. 16, 5705--5721. (Scientific Journal Ranking: 1.532, Q1).
[5] D. Ruiz, G. Vaira,Cluster solutions for the Schr\"odinger-Poisson-Slater problem around a local minimum of the potential, Rev. Mat. Iberoamericana 27 (2011) no.1, 253--271. (Scientific Journal Ranking: 1.409, Q1).
[4] G. Vaira, Semiclassical states for the nonlinear Klein-Gordon-Maxwell system, Journal of Pure and Applied Mathematics 4 (2010) no. 1, 59--96.
[3] G. Cerami, G. Vaira, Positive solutions for some nonautonomous Schrödinger-Poisson systems, Journal of Differential Equations 248 (2010), 521--543.
[2] I. Ianni, G. Vaira, Solutions of the Schr\"odinger-Poisson problem concentrating on spheres, part I: necessary conditions, Mathematical Models and Methods in Applied Sciences, Vol. 19, No. 5 (2009) 707--720.
[1] I. Ianni, G. Vaira, On concentration of positive bound states for the Schrödinger-Poisson problem with potentials, Advanced Nonlinear Studies 8 (2008) 573--595.
Atti di convegno
[1] G. Vaira, "A note on sign-changing solutions for the Schr\"odinger-Poisson", Concentration Compactness and Profile Decompositions, Trends in Mathematics, 143--156, 2014 Springer Basel AG.