@article{AIHPC_2009__26_4_1423_0, author = {D'Aprile, Teresa and Pistoia, Angela}, title = {Existence, {Multiplicity} and {Profile} of {Sign-Changing} {Clustered} {Solutions} of a {Semiclassical} {Nonlinear} {Schr\"odinger} {Equation}}, journal = {Annales de l'I.H.P. Analyse non lin\'eaire}, pages = {1423--1451}, publisher = {Elsevier}, volume = {26}, number = {4}, year = {2009}, doi = {10.1016/j.anihpc.2009.01.002}, mrnumber = {2542732}, zbl = {1173.35679}, language = {en}, url = {http://www.numdam.org/articles/10.1016/j.anihpc.2009.01.002/} }
TY - JOUR AU - D'Aprile, Teresa AU - Pistoia, Angela TI - Existence, Multiplicity and Profile of Sign-Changing Clustered Solutions of a Semiclassical Nonlinear Schrödinger Equation JO - Annales de l'I.H.P. Analyse non linéaire PY - 2009 SP - 1423 EP - 1451 VL - 26 IS - 4 PB - Elsevier UR - http://www.numdam.org/articles/10.1016/j.anihpc.2009.01.002/ DO - 10.1016/j.anihpc.2009.01.002 LA - en ID - AIHPC_2009__26_4_1423_0 ER -
%0 Journal Article %A D'Aprile, Teresa %A Pistoia, Angela %T Existence, Multiplicity and Profile of Sign-Changing Clustered Solutions of a Semiclassical Nonlinear Schrödinger Equation %J Annales de l'I.H.P. Analyse non linéaire %D 2009 %P 1423-1451 %V 26 %N 4 %I Elsevier %U http://www.numdam.org/articles/10.1016/j.anihpc.2009.01.002/ %R 10.1016/j.anihpc.2009.01.002 %G en %F AIHPC_2009__26_4_1423_0
D'Aprile, Teresa; Pistoia, Angela. Existence, Multiplicity and Profile of Sign-Changing Clustered Solutions of a Semiclassical Nonlinear Schrödinger Equation. Annales de l'I.H.P. Analyse non linéaire, Tome 26 (2009) no. 4, pp. 1423-1451. doi : 10.1016/j.anihpc.2009.01.002. http://www.numdam.org/articles/10.1016/j.anihpc.2009.01.002/
[1] On the Location and Profile of Spike-Layer Nodal Solutions to Nonlinear Schrödinger Equations, J. Math. Anal. Appl. 296 (2004) 563-577. | MR | Zbl
, ,[2] Semiclassical States of Nonlinear Schrödinger Equations, Arch. Ration. Mech. Anal. 140 (1997) 285-300. | MR | Zbl
, , ,[3] Perturbation Methods and Semilinear Elliptic Problem on , Progr. Math., vol. 240, Birkhäuser, 2005. | Zbl
, ,[4] Multiplicity Results for Some Nonlinear Schrödinger Equations With Potentials, Arch. Ration. Mech. Anal. 159 (3) (2001) 253-271. | MR | Zbl
, , ,[5] Configuration Spaces, Transfer, and 2-Nodal Solutions of a Semiclassical Nonlinear Schrödinger Equation, Math. Ann. 338 (2007) 147-185. | MR | Zbl
, , ,[6] 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. | MR | Zbl
, ,[7] Three Nodal Solutions of Singularly Perturbed Elliptic Equations on Domains Without Topology, Ann. Inst. H. Poincaré Anal. Non Linéaire 22 (2005) 259-281. | Numdam | MR | Zbl
, ,[8] On the Existence Profile of Multi-Peaked Solutions to Singularly Perturbed Semilinear Dirichlet Problems, Discrete Contin. Dynam. Systems 2 (1996) 221-236. | MR | Zbl
, , , ,[9] Sign Changing Solutions of Semilinear Elliptic Problems in Exterior Domains, Calc. Var. Partial Differential Equations 30 (2007) 353-367. | MR | Zbl
, ,[10] Infinitely Many Bound States for Some Nonlinear Scalar Field Equations, Calc. Var. Partial Differential Equations 23 (2005) 139-168. | MR | Zbl
, , ,[11] A Note on Asymptotic Uniqueness for Some Nonlinearities Which Change Sign, Bull. Austral. Math. Soc. 61 (2000) 305-312. | MR | Zbl
,[12] Multipeak Solutions for a Singular Perturbed Neumann Problem, Pacific J. Math. 189 (1999) 241-262. | MR | Zbl
, ,[13] On the Location of Spikes of Solutions With Two Sharp Layers for a Singularly Perturbed Semilinear Dirichlet Problem, J. Differential Equations 157 (1999) 82-101. | MR | Zbl
, ,[14] On the Number of Sign-Changing Solutions of a Semiclassical Nonlinear Schrödinger Equation, Adv. Differential Equations 12 (2007) 737-758. | MR
, ,[15] Local Mountain Passes for Semilinear Elliptic Problems in Unbounded Domains, Calc. Var. Partial Differential Equations 4 (1996) 121-137. | MR | Zbl
, ,[16] Multi-Peak Bound States for Nonlinear Schrödinger Equations, Ann. Inst. H. Poincaré Anal. Non Linéaire 15 (1998) 127-149. | Numdam | MR | Zbl
, ,[17] An Elementary Construction of Complex Patterns in Nonlinear Schrödinger Equations, Nonlinearity 15 (2002) 1653-1671. | MR | Zbl
, , ,[18] Multi-Peak Solutions for Some Singular Perturbation Problems, Calc. Var. Partial Differential Equations 10 (2000) 119-134. | MR | Zbl
, , ,[19] On the Role of Mean Curvature in Some Singularly Perturbed Neumann Problems, SIAM J. Math. Anal. 31 (1999) 63-79. | MR | Zbl
, , ,[20] Nonspreading Wave Pockets for the Cubic Schrödinger Equation With a Bounded Potential, J. Funct. Anal. 69 (1986) 397-408. | MR | Zbl
, ,[21] Symmetry of Positive Solutions of Nonlinear Elliptic Equations in , Adv. Math. Suppl Stud. A 7 (1981) 369-402. | MR | Zbl
, , ,[22] On the Effect of Critical Points of Distance Function in Superlinear Elliptic Problems, Adv. Differential Equations 5 (2000) 1397-1420. | MR | Zbl
, ,[23] Existence of Multipeak Solutions for a Semilinear Neumann Problem Via Nonsmooth Critical Point Theory, Calc. Var. Partial Differential Equations 11 (2000) 143-175. | MR | Zbl
, , ,[24] Multipeak Solutions for a Semilinear Neumann Problem, Duke Math. J. 84 (1996) 739-769. | MR | Zbl
,[25] Multiple Interior Peak Solutions for Some Singularly Perturbed Neumann Problems, J. Differential Equations 158 (1999) 1-27. | MR | Zbl
, ,[26] On Multiple Mixed Interior and Boundary Peak Solutions for Some Singularly Perturbed Neumann Problems, Canad. J. Math. 52 (2000) 522-538. | MR | Zbl
, ,[27] Multiple Boundary Peak Solutions for Some Singularly Perturbed Neumann Problems, Ann. Inst. H. Poincaré Anal. Non Linéaire 17 (2000) 47-82. | EuDML | Numdam | MR | Zbl
, , ,[28] On Interacting Bumps of Semiclassical States of Nonlinear Schrödinger Equations, Adv. Differential Equations 5 (2000) 899-928. | MR | Zbl
, ,[29] On a Singularly Perturbed Elliptic Equation, Adv. Differential Equations 2 (1997) 955-980. | MR | Zbl
,[30] On a Singularly Perturbed Equation With Neumann Boundary Conditions, Comm. Partial Differential Equations 23 (1998) 487-545. | MR | Zbl
,[31] On the Multiplicity of Nodal Solutions to a Singularly Perturbed Neumann Problem, Mediterranean J. Math. 5 (2008) 285-294. | MR | Zbl
, ,[32] The Dirichlet Problem for Singularly Perturbed Elliptic Equations, Comm. Pure Appl. Math. 51 (1998) 1445-1490. | MR | Zbl
, ,[33] On the Shape of Least-Energy Solutions to a Semi-Linear Neumann Problem, Duke Math. J. 70 (1993) 247-281. | MR | Zbl
, ,[34] On the Location and Profile of Spike-Layer Solutions to Singularly Perturbed Semilinear Dirichlet Problems: Intermediate Solutions, Duke Math. J. 94 (1998) 597-618. | MR | Zbl
, , ,[35] On the Location and Profile of Spike-Layer Solutions to Singularly Perturbed Semilinear Dirichlet Problems, Comm. Pure Appl. Math. 48 (1995) 731-768. | MR | Zbl
, ,[36] 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. | MR | Zbl
, ,[37] On the Existence and Profile of Nodal Solutions of Some Singularly Perturbed Semilinear Neumann Problem, Comm. Partial Differential Equations 23 (1998) 793-816. | MR | Zbl
, ,[38] On Positive Multi-Lump Bound States of Nonlinear Schrödinger Equations Under Multiple Well Potential, Comm. Math. Phys. 131 (1990) 223-253. | MR | Zbl
,[39] On Concentration of Positive Bound States of Nonlinear Schrödinger Equations, Comm. Math. Phys. 153 (1993) 229-244. | MR | Zbl
,[40] On the Boundary Spike Layer Solutions of a Singularly Perturbed Semilinear Neumann Problem, J. Differential Equations 134 (1997) 104-133. | MR | Zbl
,[41] On the Construction of Single-Peaked Solutions to a Singularly Perturbed Semilinear Dirichlet Problem, J. Differential Equations 129 (1996) 315-333. | MR | Zbl
,[42] On the Number of Nodal Solutions to a Singularly Perturbed Neumann Problem, Manuscripta Math. 117 (2005) 333-344. | MR
, ,Cité par Sources :