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research

Here is a list of my publications, as listed in AMS MathSciNet:
  1. MR1850208 (2002f:58014) Secchi, S. A note on closed geodesics for a class of non-compact Riemannian manifolds. Adv. Nonlinear Stud. 1 (2001), no. 1, 132–142. (Reviewer: Anna Maria Candela), 58E10 (53C22)
  2. MR1857674 (2002m:35044) Ambrosetti, A.; Malchiodi, A.; Secchi, S. Multiplicity results for some nonlinear Schrödinger equations with potentials. Arch. Ration. Mech. Anal. 159 (2001), no. 3, 253–271. (Reviewer: Marcel Oliver), 35J60 (35J20)
  3. MR1941775 (2003k:81062) Cingolani, Silvia; Secchi, Simone Semiclassical limit for nonlinear Schrödinger equations with electromagnetic fields. J. Math. Anal. Appl. 275 (2002), no. 1, 108–130, 81Q20 (35Q40 81V10)
  4. MR1990020 (2004d:35050) Secchi, Simone; Smets, Didier; Willem, Michel Remarks on a Hardy-Sobolev inequality. C. R. Math. Acad. Sci. Paris 336 (2003), no. 10, 811–815, 35J20 (35A30 35B05)
  5. MR2017678 (2005b:37138) Secchi, S.; Stuart, C. A. Global bifurcation of homoclinic solutions of Hamiltonian systems. Discrete Contin. Dyn. Syst. 9 (2003), no. 6, 1493–1518. (Reviewer: Thomas Bartsch), 37J45 (34C23 37J20 47H11)
  6. MR2087750 Pomponio, A.; Secchi, S. Interior spikes of a singularly perturbed Neumann problem with potentials. Appl. Math. Lett. 17 (2004), no. 9, 1025–1031, 35J60 (35B25)
  7. MR2099612 (2005h:35106) Secchi, Simone; Squassina, Marco On the location of concentration points for singularly perturbed elliptic equations. Adv. Differential Equations 9 (2004), no. 1-2, 221–239. (Reviewer: Juncheng Wei), 35J60 (35B25 35B65 58E05)
  8. MR2102664 (2005h:35104) Pomponio, A.; Secchi, S. On a class of singularly perturbed elliptic equations in divergence form: existence and multiplicity results. J. Differential Equations 207 (2004), no. 2, 229–266. (Reviewer: Juncheng Wei), 35J60 (35B25 47J30)
  9. MR2140552 (2005m:35287) Secchi, Simone; Squassina, Marco On the location of spikes for the Schrödinger equation with electromagnetic field. Commun. Contemp. Math. 7 (2005), no. 2, 251–268, 35Q55 (81Q05)
  10. MR2143013 (2006b:81081) Cingolani, Silvia; Secchi, Simone Semiclassical states for NLS equations with magnetic potentials having polynomial growths. J. Math. Phys. 46 (2005), no. 5, 053503, 19 pp. (Reviewer: Serge C. Richard), 81Q20 (35Q55)
  11. MR2274942 (2007g:35031) Secchi, Simone; Serra, Enrico Symmetry breaking results for problems with exponential growth in the unit disk. Commun. Contemp. Math. 8 (2006), no. 6, 823–839. (Reviewer: András Domokos), 35J20 (35B30 35J60 47J30)
  12. MR2279741 (2008e:35180) Barile, Sara; Cingolani, Silvia; Secchi, Simone Single-peaks for a magnetic Schrödinger equation with critical growth. Adv. Differential Equations 11 (2006), no. 10, 1135–1166. (Reviewer: Pascal Bégout), 35Q55 (35B33 47J30 58E05)
  13. MR2394119 (2010b:35158) Barutello, Vivina; Secchi, Simone; Serra, Enrico A note on the radial solutions for the supercritical Hénon equation. J. Math. Anal. Appl. 341 (2008), no. 1, 720–728, 35J65 (34B18 47J05)
  14. MR2422078 (2010g:70017) Barutello, Vivina; Secchi, Simone Morse index properties of colliding solutions to the N-body problem. Ann. Inst. H. Poincaré Anal. Non Linéaire 25 (2008), no. 3, 539–565, 70F10 (37J45 37N05)
  15. MR2436451 (2009k:35065) Calanchi, Marta; Secchi, Simone; Terraneo, Elide Multiple solutions for a Hénon-like equation on the annulus. J. Differential Equations 245 (2008), no. 6, 1507–1525. (Reviewer: Nils Ackermann), 35J60 (35B33 35J20 35J25 47J30 58E05)
  16. MR2542577 (2010h:35366) Cingolani, Silvia; Jeanjean, Louis; Secchi, Simone Multi-peak solutions for magnetic NLS equations without non-degeneracy conditions. ESAIM Control Optim. Calc. Var. 15 (2009), no. 3, 653–675. (Reviewer: S. Rajasekar), 35Q55 (35C08 47J30 81V10)
  17. MR2600460 (2011c:35544) Pomponio, Alessio; Secchi, Simone A note on coupled nonlinear Schrödinger systems under the effect of general nonlinearities. Commun. Pure Appl. Anal. 9 (2010), no. 3, 741–750. (Reviewer: Juan Campos), 35Q55 (35J91 47J30 58E05 78A60)
  18. MR2606826 (2011g:35092) Secchi, Simone A note on Schrödinger-Newton systems with decaying electric potential. Nonlinear Anal. 72 (2010), no. 9-10, 3842–3856. (Reviewer: Sarah G. Raynor), 35J47 (35B25 35B38 35J10 35J20 35J50 35J91)
  19. MR2726117 Cingolani, Silvia; Secchi, Simone; Squassina, Marco Semi-classical limit for Schrödinger equations with magnetic field and Hartree-type nonlinearities. Proc. Roy. Soc. Edinburgh Sect. A 140 (2010), no. 5, 973–1009, 35Q55 (81Q05 81Q20)
  20. MR2951722 Secchi, Simone The Brezis-Nirenberg problem for the Hénon equation: ground state solutions. Adv. Nonlinear Stud. 12 (2012), no. 2, 383–394.
  21. MR2912346 Cingolani, SilviaClapp, MónicaSecchi, Simone Multiple solutions to a magnetic nonlinear Choquard equation. Z. Angew. Math. Phys. 63 (2012), no. 2, 233–248.
  22. MR2958344 Secchi, Simone Increasing variational solutions for a nonlinear p-Laplace equation without growth conditions. Ann. Mat. Pura Appl. (4) 191 (2012), no. 3, 469–485.
  23. MR3059423 Secchi, Simone Ground state solutions for nonlinear fractional Schrödinger equations in N. J. Math. Phys.54 (2013), no. 3, 031501, 17 pp.
  24. MR3099989 Secchi, Simone Perturbation results for some nonlinear equations involving fractional operators. Differ. Equ. Appl. (2013), no. 2, 221–236.
  25. S. Cingolani, S. Secchi, Multiple $\mathbb{S}^{1}$--orbits for the Schrödinger-Newton system. Differential and Integral Equations 26 (2013), 867-884.
  26. S. Secchi, M. Squassina. Soliton dynamics for fractional Schrödinger equations. Applicable Analysis 93 (2014), 1702-1729.
  27. S. Secchi, On fractional Schrödinger equations in $\mathbb{R}^N$ without the Ambrosetti-Rabinowitz condition. Topological Methods in Nonlinear Analysis 47 (2016), 19-41.
  28. S. Cingolani, M. Clapp, S. Secchi, Intertwining semiclassical solutions to a Schrödinger-Newton system. DCDS-S 6 (2013), 891-908. http://arxiv.org/abs/1110.4213
  29. S. Cingolani, S. Secchi, Ground states for the pseudo-relativistic Hartree equation with external potential. Proc. Roy. Soc. Edinburgh Sect. A 145 (2015), 73-90.
  30. S. Secchi, N. Shioji, M. Squassina, Coron problem for fractional equations. Differential and Integral equations 28 (2015), 103-118.
  31. S. Secchi, S. Cingolani, Semiclassical analysis for pseudo-relativistic Hartree equations. Journal of Differential Equations 258 (2015), no. 15, 4156-4179. http://dx.doi.org/10.1016/j.jde.2015.01.029
  32. S. Secchi, On some nonlinear fractional equations involving the Bessel operator. To appear in Journal of Dynamics and Differential Equations.
  33. S. Secchi, Concave-convex nonlinearities for some nonlinear fractional equations involving the Bessel operator. Complex variables and elliptic equations, in press. http://dx.doi.org/10.1080/17476933.2016.1234465
  34. S. Secchi, Existence of solutions for a semirelativistic Hartree equation with unbounded potentials. Submitted. https://arxiv.org/abs/1701.02885
You can download almost every paper from my personal arXiv site
http://arxiv.org/a/secchi_s_1

Preprints

Theses and lecture notes

  • S. Secchi, Nonlinear differential equations on noncompact domains, Ph.D Thesis, Ps-file
  • S. Secchi, Introduzione a un metodo perturbativo nella teoria dei punti critici. Note di un ciclo di seminari presso il Dipartimento di Matematica dell'Università di Pisa, aprile/maggio 2003. PDF file

Book
S. Secchi. Lezioni di analisi infinitesimale. Liguori editore, 2013.
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