Existence, multiplicity and profile of sign-changing clustered solutions of a semiclassical nonlinear Schrödinger equation

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1. [1] Alves C.O., Soares S.H.M., On the location and profile of spike-layer nodal solutions to nonlinear Schrödinger equations, J. Math. Anal. Appl.296 (2004) 563-577. Zbl1051.35081MR2075185
2. [2] Ambrosetti A., Badiale M., Cingolani S., Semiclassical states of nonlinear Schrödinger equations, Arch. Ration. Mech. Anal.140 (1997) 285-300. Zbl0896.35042MR1486895
3. [3] Ambrosetti A., Malchiodi A., Perturbation Methods and Semilinear Elliptic Problem on $R^N$, Progr. Math., vol. 240, Birkhäuser, 2005. Zbl1115.35004
4. [4] Ambrosetti A., Malchiodi A., Secchi S., Multiplicity results for some nonlinear Schrödinger equations with potentials, Arch. Ration. Mech. Anal.159 (3) (2001) 253-271. Zbl1040.35107MR1857674
5. [5] Bartsch T., Clapp M., Weth T., Configuration spaces, transfer, and 2-nodal solutions of a semiclassical nonlinear Schrödinger equation, Math. Ann.338 (2007) 147-185. Zbl1126.35061MR2295508
6. [6] Bartsch T., Weth T., The effect of the domain's configuration space on the number of nodal solutions of singularly perturbed elliptic equations, Topol. Methods Nonlinear Anal.26 (2005) 109-133. Zbl1152.35039MR2179353
7. [7] Bartsch T., Weth T., Three nodal solutions of singularly perturbed elliptic equations on domains without topology, Ann. Inst. H. Poincaré Anal. Non Linéaire22 (2005) 259-281. Zbl1114.35068MR2136244
8. [8] Cao D., Dancer E.N., Noussair E., Yan S., On the existence profile of multi-peaked solutions to singularly perturbed semilinear Dirichlet problems, Discrete Contin. Dynam. Systems2 (1996) 221-236. Zbl0947.35073MR1382508
9. [9] Cerami G., Clapp M., Sign changing solutions of semilinear elliptic problems in exterior domains, Calc. Var. Partial Differential Equations30 (2007) 353-367. Zbl1174.35026MR2332418
10. [10] Cerami G., Devillanova G., Solimini S., Infinitely many bound states for some nonlinear scalar field equations, Calc. Var. Partial Differential Equations23 (2005) 139-168. Zbl1078.35113MR2138080
11. [11] Dancer E.N., A note on asymptotic uniqueness for some nonlinearities which change sign, Bull. Austral. Math. Soc.61 (2000) 305-312. Zbl0945.35031MR1748710
12. [12] Dancer E.N., Yan S., Multipeak solutions for a singular perturbed Neumann problem, Pacific J. Math.189 (1999) 241-262. Zbl0933.35070MR1696122
13. [13] Dancer E.N., Wei J., On the location of spikes of solutions with two sharp layers for a singularly perturbed semilinear Dirichlet problem, J. Differential Equations157 (1999) 82-101. Zbl1087.35507MR1710015
14. [14] D'Aprile T., Pistoia A., On the number of sign-changing solutions of a semiclassical nonlinear Schrödinger equation, Adv. Differential Equations12 (2007) 737-758. Zbl1207.35040MR2331522
15. [15] Del Pino M., Felmer P., Local mountain passes for semilinear elliptic problems in unbounded domains, Calc. Var. Partial Differential Equations4 (1996) 121-137. Zbl0844.35032MR1379196
16. [16] Del Pino M., Felmer P., Multi-peak bound states for nonlinear Schrödinger equations, Ann. Inst. H. Poincaré Anal. Non Linéaire15 (1998) 127-149. Zbl0901.35023MR1614646
17. [17] Del Pino M., Felmer P., Tanaka K., An elementary construction of complex patterns in nonlinear Schrödinger equations, Nonlinearity15 (2002) 1653-1671. Zbl1022.34037MR1925432
18. [18] Del Pino M., Felmer P., Wei J., Multi-peak solutions for some singular perturbation problems, Calc. Var. Partial Differential Equations10 (2000) 119-134. Zbl0974.35041MR1750734
19. [19] Del Pino M., Felmer P., Wei J., On the role of mean curvature in some singularly perturbed Neumann problems, SIAM J. Math. Anal.31 (1999) 63-79. Zbl0942.35058MR1742305
20. [20] Floer A., Weinstein A., Nonspreading wave pockets for the cubic Schrödinger equation with a bounded potential, J. Funct. Anal.69 (1986) 397-408. Zbl0613.35076MR867665
21. [21] Gidas B., Ni W.M., Nirenberg L., Symmetry of positive solutions of nonlinear elliptic equations in $R^N$, Adv. Math. Suppl Stud. A7 (1981) 369-402. Zbl0469.35052MR634248
22. [22] Grossi M., Pistoia A., On the effect of critical points of distance function in superlinear elliptic problems, Adv. Differential Equations5 (2000) 1397-1420. Zbl0989.35054MR1785679
23. [23] Grossi M., Pistoia A., Wei J., Existence of multipeak solutions for a semilinear Neumann problem via nonsmooth critical point theory, Calc. Var. Partial Differential Equations11 (2000) 143-175. Zbl0964.35047MR1782991
24. [24] Gui C., Multipeak solutions for a semilinear Neumann problem, Duke Math. J.84 (1996) 739-769. Zbl0866.35039MR1408543
25. [25] Gui C., Wei J., Multiple interior peak solutions for some singularly perturbed Neumann problems, J. Differential Equations158 (1999) 1-27. Zbl1061.35502MR1721719
26. [26] Gui C., Wei J., On multiple mixed interior and boundary peak solutions for some singularly perturbed Neumann problems, Canad. J. Math.52 (2000) 522-538. Zbl0949.35052MR1758231
27. [27] Gui C., Wei J., Winter M., Multiple boundary peak solutions for some singularly perturbed Neumann problems, Ann. Inst. H. Poincaré Anal. Non Linéaire17 (2000) 47-82. Zbl0944.35020MR1743431
28. [28] Kang X., Wei J., On interacting bumps of semiclassical states of nonlinear Schrödinger equations, Adv. Differential Equations5 (2000) 899-928. Zbl1217.35065MR1776345
29. [29] Li Y.Y., On a singularly perturbed elliptic equation, Adv. Differential Equations2 (1997) 955-980. Zbl1023.35500MR1606351
30. [30] Li Y.Y., On a singularly perturbed equation with Neumann boundary conditions, Comm. Partial Differential Equations23 (1998) 487-545. Zbl0898.35004MR1620632
31. [31] Micheletti A.M., Pistoia A., On the multiplicity of nodal solutions to a singularly perturbed Neumann problem, Mediterranean J. Math.5 (2008) 285-294. Zbl1207.35037MR2465576
32. [32] Li Y.Y., Nirenberg L., The Dirichlet problem for singularly perturbed elliptic equations, Comm. Pure Appl. Math.51 (1998) 1445-1490. Zbl0933.35083MR1639159
33. [33] Ni W.M., Takagi I., On the shape of least-energy solutions to a semi-linear Neumann problem, Duke Math. J.70 (1993) 247-281. Zbl0796.35056MR1219814
34. [34] Ni W.M., Takagi I., Wei J., On the location and profile of spike-layer solutions to singularly perturbed semilinear Dirichlet problems: intermediate solutions, Duke Math. J.94 (1998) 597-618. Zbl0946.35007MR1639546
35. [35] Ni W.M., Wei J., On the location and profile of spike-layer solutions to singularly perturbed semilinear Dirichlet problems, Comm. Pure Appl. Math.48 (1995) 731-768. Zbl0838.35009MR1342381
36. [36] Noussair E., Wei J., On the effect of domain geometry on the existence and profile of nodal solutions of some singularly perturbed semilinear Dirichlet problem, Indiana Univ. Math. J.46 (1997) 1255-1272. Zbl0907.35011MR1631584
37. [37] Noussair E., Wei J., On the existence and profile of nodal solutions of some singularly perturbed semilinear Neumann problem, Comm. Partial Differential Equations23 (1998) 793-816. Zbl0914.35012MR1632748
38. [38] Oh Y.-G., On positive multi-lump bound states of nonlinear Schrödinger equations under multiple well potential, Comm. Math. Phys.131 (1990) 223-253. Zbl0753.35097MR1065671
39. [39] Wang X., On concentration of positive bound states of nonlinear Schrödinger equations, Comm. Math. Phys.153 (1993) 229-244. Zbl0795.35118MR1218300
40. [40] Wei J., On the boundary spike layer solutions of a singularly perturbed semilinear Neumann problem, J. Differential Equations134 (1997) 104-133. Zbl0873.35007MR1429093
41. [41] Wei J., On the construction of single-peaked solutions to a singularly perturbed semilinear Dirichlet problem, J. Differential Equations129 (1996) 315-333. Zbl0865.35011MR1404386
42. [42] Wei J., Weth T., On the number of nodal solutions to a singularly perturbed Neumann problem, Manuscripta Math.117 (2005) 333-344. Zbl1205.35031MR2154254