Metodi variazionali e topologici nello studio delle equazioni di Schrödinger nonlineari agli stati stazionari

 Access to full text

 Full (PDF)

 Full (DjVu)

1. AKHMEDIEV, N. N., Novel class of nonlinear surface waves, Asymmetric modes in a symmetric layered structure, Sov. Phys. JEPT, 56 (1982), 299-303. 
2. ANGENENT, S., The Shadowing Lemma for Elliptic PDE, Dynamics of Infinite Dimensional Systems (S. N. Chow and J. K. Hale eds.), F37 (1987). Zbl0653.35030MR921893
3. AMBROSETTI, A.- ARCOYA, D.- GÁMEZ, J. L., Asymmetric bound states of differential equations in Nonlinear Optics, Rend. Sem. Mat. Padova, 100 (1998), 231-247. Zbl0922.34020MR1675283
4. AMBROSETTI, A.- BADIALE, M., Homoclinics: Poincaré-Melnikov type results via a variational approach, Ann. Inst. H. Poincaré, Anal. Nonlin., 15 (1998), 233-252. Zbl1004.37043MR1614571
5. AMBROSETTI, A.- BADIALE, M.- CINGOLANI, S., Semiclassical states of nonlinear Schrödinger equations with bounded potentials, Rendiconti dell'Accademia Nazionale dei Lincei, ser. IX, 7 (1996), 155-160. Zbl0872.35098MR1454410
6. AMBROSETTI, A.- BADIALE, M.- CINGOLANI, S., Semiclassical states of nonlinear Schrödinger equations, Arch. Rat. Mech. Anal., 140 (1997), 285-300. Zbl0896.35042MR1486895
7. AMBROSETTI, A.- COTI ZELATI, V.- EKELAND, I., Symmetry breaking in Hamiltonian systems, J. Diff. Eq., 67 (1987), 165-184. Zbl0606.58043MR879691
8. ARCOYA, D.- CINGOLANI, S.- GÁMEZ, J. L., Asymmetric modes in symmetric nonlinear optical waveguides, SIAM Math. Anal., 30 (1999), 1391-1400. Zbl0933.34014MR1718307
9. BARTSCH, T.- WANG, Z. Q., Existence and multiplicity results for some superlinear elliptic problems on ${\mathbb{R}}^N$, Comm. Part. Diff. Eq., 20 (1995), 1725-1741. Zbl0837.35043MR1349229
10. BENCI, V.- CERAMI, G., The effect of the domain topology on the number of positive solutions of nonlinear elliptic problems, Arch. Rat. Mech. Anal., 114 (1991), 79-93. Zbl0727.35055MR1088278
11. BENCI, V.- CERAMI, G., Multiple positive solutions of some elliptic problems via the Morse theory and the domain topology, Calc. Var., 2 (1994), 29-48. Zbl0822.35046MR1384393
12. BENCI, V.- CERAMI, G.- PASSASEO, D., On the number of the positive solutions of some nonlinear elliptic problems, Nonlinear Analysis, A tribute in honour of G. Prodi, Quaderno Scuola Norm. Sup., Pisa1991, 93-107. Zbl0838.35040MR1205376
13. BERESTYCKI, H.- LIONS, P. L., Nonlinear scalar field equations, I - Existence of a ground state, Arch. Rat. Mech. Anal., 82 (1983), 313-375. Zbl0533.35029MR695535
14. BREZIS, H.- NIRENBERG, L., Positive solutions of nonlinear elliptic equations involving critical Sobolev exponents, Comm. Pure Appl. Math., 36 (1983), 437-477. Zbl0541.35029MR709644
15. CINGOLANI, S., On a perturbed semilinear elliptic equation in ${\mathbb{R}}^N$, Comm. Applied Anal., 3 (1999), 49-57. Zbl0922.35051MR1669769
16. CINGOLANI, S., Positive solutions to perturbed elliptic problems in ${\mathbb{R}}^N$ involving critical Sobolev exponent, to appear on Nonlinear Analysis, T.M.A. Zbl1097.35047MR1880579
17. CINGOLANI, S.- GÁMEZ, J. L., Asymmetric positive solutions for a symmetric nonlinear problem in ${\mathbb{R}}^N$, Calc. Var. PDE, 11 (2000), 97-117. Zbl0968.35043MR1777465
18. CINGOLANI, S.- LAZZO, M., Multiple semiclassical standing waves for a class of nonlinear Schrödinger equations, Top. Meth. Nonlinear Anal., 10 (1997), 1-13. Zbl0903.35018MR1646619
19. CINGOLANI, S.- LAZZO, M., Multiple positive solutions to nonlinear Schrödinger equations with competing potential functions, J. Diff. Eq., 160 (2000), 118-138. Zbl0952.35043MR1734531
20. CINGOLANI, S.- NOLASCO, M., Multi-peak periodic semiclassical states of nonlinear Schrödinger equations, Proc. Royal Soc. Edin., 128 A (1998), 1249-1260. Zbl0922.35158MR1664105
21. CORON, J. M., Topologie et cas limite des injections de Sobolev, C.R.A.S., Ser. I, 299 (1984), 209-212. Zbl0569.35032MR762722
22. COTI ZELATI, V.- ESTEBAN, M. J., Symmetry breaking and multiple solutions for a Neumann problem in an exterior domain, Proc. Royal Soc. Edin., 116A (1990), 327-339. Zbl0748.35012MR1084737
23. COTI ZELATI, V.- RABINOWITZ, P., Homoclinic orbits for second order Hamiltonian systems possessing superquadratic potentials, J. Amer. Math. Soc., 4 (1991), 693-727. Zbl0744.34045MR1119200
24. COTI ZELATI, V.- RABINOWITZ, P., Homoclinics type solutions for a semilinear elliptic PDE on ${\mathbb{R}}^N$, Comm. Pure Appl. Math., 45 (1992), 1217-1269. Zbl0785.35029MR1181725
25. FLOER, A.- WEINSTEIN, A., Nonspreading wave packets for the cubic Schrödinger equation with a bounded potential, J. Funct. Anal., 69 (1986), 397-408. Zbl0613.35076MR867665
26. DEL PINO, M.- FELMER, P. L., Local mountain pass for semilinear elliptic problems in unbounded domains, Calc. Var. PDE, 4 (1996), 121-137. Zbl0844.35032MR1379196
27. DEL PINO, M.- FELMER, P. L., Semiclassical states of nonlinear Schrödinger equations, J. Func. Anal., 149 (1997), 245-265. Zbl0887.35058MR1471107
28. DEL PINO, M.- FELMER, P. L., Multi-peak bound states of nonlinear Schrödinger equations, Ann. Inst. H. Poincarè, Anal. Nonlin., 15 (1998), 127-149. Zbl0901.35023MR1614646
29. ESTEBAN, M. J., Nonsymmetric ground states of symmetric variational problems, Comm. Pure Appl. Math., 44 (1991), 259-274. Zbl0826.49002MR1085830
30. GIDAS, B.- NI, W. M.- NIREMBERG, L., Symmetry of positive solutions of nonlinear elliptic equations in ${\mathbb{R}}^N$, Math. Analysis Appl., Part A 7 (1981), 369-402. Zbl0469.35052
31. GRILLAKIS, M.- SHATAH, J.- STRAUSS, W., Stability theory of solitary waves in the presence of symmetry, I, J. Funct. Anal., 74 (1987), 160-197. Zbl0656.35122MR901236
32. GROSSI, M., Some recent results on a class of nonlinear Schrödinger equations, to appear on Math. Z. Zbl0970.35039MR1801580
33. GUI, C., Existence of multi-bumps solutions for nonlinear Schrödinger equations via variational methods, Comm. Part. Diff. Eq., 21 (1996), 787-820. Zbl0857.35116MR1391524
34. JOHN, O.- STUART, C., Guidance properties of a cylindrical defocusing waveguide, Comm. Math. Univ. Carolinae, 35 (1994), 653-673. Zbl0819.35137MR1321236
35. KWONG, M. K., Uniqueness of $\mathrm{\Delta }u-u+u^p=0$ in ${\mathbb{R}}^N$, Arch. Rat. Mech. Anal., 105 (1989), 243-266. Zbl0676.35032MR969899
36. LI, Y. Y., On a singularly perturbed elliptic equation, Adv. Diff. Eq., 2 (1997), 955-980. Zbl1023.35500MR1606351
37. LI, Y., Remarks on a semilinear elliptic equation on ${\mathbb{R}}^n$, J. Diff. Eqs., 74 (1988), 34-49. Zbl0662.35038MR949624
38. OH, Y. G., Existence of semiclassical bound states of nonlinear Schrödinger with potential in the class ${\left(V\right)}_a$, Comm. Part. Diff. Eq., 13 (1988), 1499-1519. Zbl0702.35228MR970154
39. OH, Y. G., On positive multi-bump states of nonlinear Schrödinger equation under multiple well potentials, Comm. Math. Phys., 131 (1990), 223-253. Zbl0753.35097MR1065671
40. RABINNOWITZ, P., On a class of nonlinear Schrödinger equations, ZAMP, 43 (1992), 27-42. MR1162728
41. RUPPEN, H., Multiple TE-Modes for planar self-focusing wave guides, Ann. Mat. Pura Appl., (IV) CLXXII (1997), 323-377. Zbl0937.78012MR1621183
42. SÉRÉ, E., Existence of infinitely many homoclinic orbits in Hamiltonian systems, Math. Z., 209 (1992), 27-42. Zbl0725.58017MR1143210
43. STUART, C., Self-trapping of an electromagnetic field and bifurcation from the essential spectrum, Arch. Rational Mech. Anal., 113 (1991), 65-96. Zbl0745.35044MR1079182
44. STUART, C., Guidance properties of nonlinear planar waveguided, Arch. Rational Mech. Anal., 125 (1993), 145-200. Zbl0801.35136MR1245069
45. STUART, C., The principle branch of solutions of a nonlinear elliptic eigenvalue problem in ${\mathbb{R}}^N$, J. Diff. Eqs., 124 (1996), 279-301. Zbl0842.35029MR1370142
46. WANG, X., On a concentration of positive bound states of nonlinear Schrödinger equations, Comm. Math. Phys., 153 (1993), 223-243. Zbl0795.35118MR1218300
47. WANG, X.- ZENG, B., On concentration of positive bound states of nonlinear Schrödinger equations with competing potential functions, SIAM J. Math. Anal., 28 (1997), 633-655. Zbl0879.35053MR1443612