Publications

Preprints

[42] N. Abatangelo, A. Saldaña and H. Tavares, An asymptotic relationship between Lane-Emden systems and the 1-bilaplacian equation, arXiv:2312.16696 (2023), 28 pp.

[41] P. Andrade, E. Moreira dos Santos, M. Santos and H. Tavares, Spectral partition problems with volume and inclusion constraints. arXiv:2305.02870

Publications

[40] H. Tavares, Topics in elliptic problems: from semilinear equations to shape optimization, arXiv:2311.08997, accepted in Comm. in Mathematics. (survey paper)

[39] F. Agostinho, S. Correia and H. Tavares. Classification and stability of positive solutions to the NLS equation on the T-metric graph. Nonlinearity (2024)

[38] Monica Clapp, Angela Pistoia and Hugo Tavares, Yamabe systems, optimal partitions, and nodal solutions to the Yamabe equation, accepted in Journal of the European Mathematical Society. arXiv:2106.00579  (2021), 49 pp.         

[37] Manuel Dias and Hugo Tavares, Optimal uniform bounds for competing variational elliptic systems with variable coefficients,  Nonlinear Analysis 235(2023), Paper No. 113348, 59 pp.

[36] Angela Pistoia, Delia Schiera and Hugo Tavares, Existence of solutions on the critial hyperbola for a pure Lane-Emden system with Neumann boundary conditions,  accepted in International Mathematics Research Notices, 2023

[35] Angela Pistoia, Alberto Saldaña and Hugo Tavares, Existence of solutions to a slightly supercritical pure Neumann problem,accepted in SIAM Journal on Mathematical Analysis (SIMA), 2023.

[34]  Ederson Moreira dos Santos, Gabrielle Nornberg, Delia Schiera, Hugo Tavares, Principal spectral curves for Lane-Emden fully nonlinear type systems and applications. Calc. Var. Partial Differential Equations 62 (2023), no. 2, Paper No. 49.

[33] Nicola Soave, Hugo Tavares and Alessandro Zilio, Free boundary problems with long-range interactions: uniform Lipschitz estimates in the radius. Mathematische Annalen (2022), https://doi.org/10.1007/s00208-022-02406-8

[32] Hugo Tavares, Song You and Wenming Zou, Least energy positive solutions of critical Schrödinger systems with mixed competition and cooperation terms: the higher dimensional case. Journal of Functional Analysis 283 (2022), issue 2,109497 .

[31] A. Saldaña, H. Tavares, On the least-energy solutions of the pure Neumann Lane-Emden equation, NoDEA - Nonlinear Differential Equations and Applications 29, Article number: 30 (2022).

[30] D. Bonheure, E. Moreira dos Santos, E. Parini, H. Tavares, T. Weth,  Nodal solutions for sublinear-type problems with Dirichlet boundary conditions, International Mathematics Research Notices 2022 (2022), Issue 5, Pages 3760–3804.

[29] H. Tavares, A. Zilio, Regularity of all minimizers of a class of spectral partition problems, Mathematics in Engineering 3 (2021), no. 1, Paper no. 2, 31 pp.

[28] J.P. Dias, F. Oliveira, H. Tavares, On a coupled system of a Ginzburg-Landau equation with a quasilinear conservation law, Communications in Contemporary Mathematics 22 (2020), no. 7, 1950054, 30pp.

[27] D. Cassani, H. Tavares, J. Zhang, Bose fluids and positive solutions to weakly coupled systems with critical growth in dimension two, Journal of Differential Equations 269 (2020), 2328-2385.

[26] A. Pistoia, N. Soave, H. Tavares, A fountain of positive bubbles on a Coron's problem for a competitive weakly coupled gradient system, Journal de Mathématiques Pures et Appliquées 135 (2020), 159-198.  

[25] H. Tavares and S. You, Existence of least energy positive solutions to Schrödinger systems with mixed competition and cooperation terms: the critical case, Calc. Var. Partial Differential Equations 59 (2020), no. 1, Paper No. 26.

[24] M. Grossi, A. Saldaña, H. Tavares, Sharp concentration estimates near criticality for radial sign-changing solutions of Dirichlet and Neumann problems, Proc. of the London Math. Soc. 120 (2020), 39–64. 

[23] B. Noris, H. Tavares, G. Verzini, Normalized solutions for Nonlinear Schrödinger systems on bounded domains, Nonlinearity 32 (2019), 1044–1072 

[22] A. Saldaña, H. Tavares, Least energy nodal solutions of Hamiltonian elliptic systems with Neumann boundary conditions,  Journal of Differential Equations 265 (2018), 6127-6165

[21] D. Bonheure, J. Földes, E. Moreira dos Santos, A. Saldaña, H. Tavares, Paths to uniqueness of critical points and applications to partial differential equations, Transactions of the American Math Society 370 (2018), 7081–7127 

[20] N. Soave, H. Tavares, S. Terracini, A. Zilio, Variational problems with long-range interaction, Arch. Rational Mech. Anal. 228 (2018), 743–772.

[19] A. Pistoia, H. Tavares, Spiked solutions for Schrödinger systems with Sobolev criticalexponent: the cases of competitive and weakly cooperative interactions, J. Fixed Point Theory Appl., 19 (2017), in honor of Paul Rabinowitz, 407-446.

[18] S. Correia, F. Oliveira, H. Tavares, Semitrivial vs. fully nontrivial ground states incooperative cubic Schrödinger systems with d ≥ 3 equations, Journal of Functional Analysis, 271 (2016), 2247–2273. 

[17] F. Oliveira, H. Tavares, Ground States for a nonlinear Schrödinger system with sublinearcoupling terms, Advanced Nonlinear Studies, 16 (2016), 381–387. 

[16] N. Soave, H. Tavares, New existence and symmetry results for least energy positive solutionsof Schrödinger systems with mixed competition and cooperation terms, Journal of Differential Equations 261 (2016), 505–537.  

[15] Nicola Soave, Hugo Tavares, Susanna Terracini, Alessandro Zilio, Hölder bounds and regularity of emerging free boundaries for strongly competing Schrödinger equations withnontrivial grouping, Nonlinear Analysis: Theory, Methods & Applications 138, in honor of Juan Luis Vázquez for his 70th birthday (2016), 388–427. 

[14] M. Ramos, H. Tavares, S. Terracini, Extremality conditions and regularity of solutions tooptimal partition problems involving Laplacian eigenvalues, Arch. Rational Mech. Anal. 220 (2016), 363–443.

[13] D. Bonheure, E. Moreira dos Santos, M. Ramos, H. Tavares, Existence and symmetry of least energy nodal solutions for Hamiltonian elliptic systems, J. Math. Pures Appl., 104 (2015), 1075–1107 

[12] B. Noris, H. Tavares, G. Verzini, Stable solitary waves with prescribed L^2-mass for thecubic Schrödinger system with trapping potentials, Discrete Contin. Dyn. Syst. - Ser. A, 35 (2015), 5869–5877.

[11] B. Noris, H. Tavares, G. Verzini, Existence and orbital stability of the ground states withprescribed mass for the L2-critical and supercritical NLS on bounded domains, Analysis & PDE, 7-8 (2014), 1807–1838.

[10] D. Bonheure, E. Moreira dos Santos, H. Tavares, Hamiltonian elliptic systems: a guideto variational frameworks, Portugaliae Mathematica 71, no.3, special issue dedicated to the memory of Miguel Ramos (2014), 301–395.

[9] J. F. Rodrigues, H. Tavares, Increasing powers in a degenerate parabolic logistic equation, Chinese Annals of Mathematics - ser. B 34, no.2, special issue in honor of the scientific heritage of Jacques-Louis Lions, (2013), 277–294.

[8] H. Tavares, T. Weth, Existence and symmetry results for competing variational systems, NoDEA - Nonlinear Diff. Equations and Appl. 20, no.3 (2013), 715-740.

[7] H. Tavares, S. Terracini, Regularity of the nodal set of segregated critical configurations under a weak reflection law, Calc. Var. Partial Differential Equations 45 (2012), no. 3-4, 273–317.

[6] B. Noris, H. Tavares, S. Terracini, G. Verzini, Convergence of minimax and continuationof critical points for singularly perturbed systems, Journal of the European Mathematical Society 14 (2012), 1245–1273.

[5] H. Tavares, S. Terracini, Sign-changing solutions of competition-diffusion elliptic systemsand optimal partition problems, Ann. Inst. Henri Poincaré - AN 29 (2012), 279–300.

[4] H. Tavares, S. Terracini, G. Verzini, T. Weth, Existence and nonexistence of entire solutions for non-cooperative cubic elliptic systems, Comm. in Partial Differential Equations 36 (2011), 1988–2010.

[3] B. Noris, H. Tavares, S. Terracini, G. Verzini, Uniform Holder bounds for nonlinear Schrödinger systems with strong competition, Comm. Pure Appl. Math. 63 (2010), 267–302.

[2] M. Ramos, H. Tavares, W. Zou, A Bahri-Lions theorem revisited, Adv. Math. 222 (2009), 2173–2195.

[1] M. Ramos, H. Tavares, Solutions with multiple spike patterns for an elliptic system, Calc. Var. Partial Differential Equations 31 (2008), 1–25. 

Thesis

PhD Thesis: Nonlinear elliptic systems with a variational structure: existence, asymptotics and other qualitative properties (December 2010). In this thesis you can find more detailed versions of the papers [1-3], [5], [6].

Master Thesis (in portuguese): Sobre a concentração de soluções em equações e sistemas elípticos sobrelineares (December 2006)