메뉴 건너뛰기




Volumn 15, Issue 6, 2005, Pages 1162-1222

Concentration at curves for a singularly perturbed Neumann problem in three-dimensional domains

(1)  Malchiodi, A a  

a SISSA   (Italy)

Author keywords

[No Author keywords available]

Indexed keywords


EID: 32344453066     PISSN: 1016443X     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00039-005-0542-7     Document Type: Article
Times cited : (65)

References (42)
  • 1
    • 84980075953 scopus 로고
    • Estimates near the boundary for solutions of elliptic partial differential equations satisfying general boundary conditions, I
    • [ADN]
    • [ADN] S. AGMON, A. DOUGLIS, L. NIRENBERG, Estimates near the boundary for solutions of elliptic partial differential equations satisfying general boundary conditions, I, Comm. Pure Appl. Math. 12 (1959), 623-727.
    • (1959) Comm. Pure Appl. Math. , vol.12 , pp. 623-727
    • Agmon, S.1    Douglis, A.2    Nirenberg, L.3
  • 2
    • 0031313734 scopus 로고    scopus 로고
    • Semiclassical states of nonlinear Schrödinger equations
    • [AmBC]
    • [AmBC] A. AMBROSETTI, M. BADIALE, S. CINGOLANI, Semiclassical states of nonlinear Schrödinger equations, Arch. Rational Mech. Anal. 140 (1997), 285-300.
    • (1997) Arch. Rational Mech. Anal. , vol.140 , pp. 285-300
    • Ambrosetti, A.1    Badiale, M.2    Cingolani, S.3
  • 3
    • 0038609648 scopus 로고    scopus 로고
    • Singularly perturbed elliptic equations with symmetry: Existence of solutions concentrating on spheres, Part I
    • [AmMN1]
    • [AmMN1] A. AMBROSETTI, A. MALCHIODI, W.M. Ni, Singularly perturbed elliptic equations with symmetry: Existence of solutions concentrating on spheres, Part I, Comm. Math. Phys. 235 (2003), 427-466.
    • (2003) Comm. Math. Phys. , vol.235 , pp. 427-466
    • Ambrosetti, A.1    Malchiodi, A.2    Ni, W.M.3
  • 4
    • 3042688938 scopus 로고    scopus 로고
    • Singularly perturbed elliptic equations with symmetry: Existence of solutions concentrating on spheres, Part II
    • [AmMN2]
    • [AmMN2] A. AMBROSETTI, A. MALCHIODI, W.M. Ni, Singularly perturbed elliptic equations with symmetry: Existence of solutions concentrating on spheres, Part II, Indiana Univ. Math. J. 53:2 (2004), 297-329.
    • (2004) Indiana Univ. Math. J. , vol.53 , Issue.2 , pp. 297-329
    • Ambrosetti, A.1    Malchiodi, A.2    Ni, W.M.3
  • 5
    • 0036604518 scopus 로고    scopus 로고
    • Concentration around a sphere for a singularly perturbed Schrödinger equation
    • [BD]
    • [BD] M. BADIALE, T. D'APRILE, Concentration around a sphere for a singularly perturbed Schrödinger equation, Nonlinear Anal. Ser. A: Theory Methods 49:7 (2002), 947-985.
    • (2002) Nonlinear Anal. Ser. A: Theory Methods , vol.49 , Issue.7 , pp. 947-985
    • Badiale, M.1    D'Aprile, T.2
  • 6
    • 0036752380 scopus 로고    scopus 로고
    • The semiclassical limit of the nonlinear Schrödinger equation in a radial potential
    • [BeD]
    • [BeD] V. BENCI, T. D'APRILE, The semiclassical limit of the nonlinear Schrödinger equation in a radial potential, J. Differential Equations 184: 1 (2002), 109-138.
    • (2002) J. Differential Equations , vol.184 , Issue.1 , pp. 109-138
    • Benci, V.1    D'Aprile, T.2
  • 7
    • 0002342492 scopus 로고    scopus 로고
    • Effect of symmetry to the structure of positive solutions in nonlinear elliptic problems
    • [By]
    • [By] J. BYEON, Effect of symmetry to the structure of positive solutions in nonlinear elliptic problems, J. Diff. Eq. 163:2 (2000), 429-474.
    • (2000) J. Diff. Eq. , vol.163 , Issue.2 , pp. 429-474
    • Byeon, J.1
  • 8
    • 0000650326 scopus 로고    scopus 로고
    • Multipeak solutions for a singularly perturbed Neumann problem
    • [DY]
    • [DY] E.N. DANCER., S. YAN, Multipeak solutions for a singularly perturbed Neumann problem, Pacific J. Math. 189:2 (1999), 241-262.
    • (1999) Pacific J. Math. , vol.189 , Issue.2 , pp. 241-262
    • Dancer, E.N.1    Yan, S.2
  • 9
    • 2342426289 scopus 로고    scopus 로고
    • On a class of solutions with non-vanishing angular momentum for nonlinear Schrdinger equations
    • [D']
    • [D'] T. D'APRILE, On a class of solutions with non-vanishing angular momentum for nonlinear Schrdinger equations, Diff. Int. Equ. 16:3 (2003), 349-384.
    • (2003) Diff. Int. Equ. , vol.16 , Issue.3 , pp. 349-384
    • D'Aprile, T.1
  • 10
    • 0001341199 scopus 로고    scopus 로고
    • Local mountain passes for semilinear elliptic problems in unbounded domains
    • [DeF1]
    • [DeF1] M. DEL PINO, P. FELMER, Local mountain passes for semilinear elliptic problems in unbounded domains, Calc. Var. 4 (1996), 121-137.
    • (1996) Calc. Var. , vol.4 , pp. 121-137
    • Del Pino, M.1    Felmer, P.2
  • 11
    • 0031237479 scopus 로고    scopus 로고
    • Semi-classical states for nonlinear schroedinger equations
    • [DeF2]
    • [DeF2] M. DEL PINO, P. FELMER, Semi-classical states for nonlinear schroedinger equations, J. Funct. Anal. 149 (1997), 245-265.
    • (1997) J. Funct. Anal. , vol.149 , pp. 245-265
    • Del Pino, M.1    Felmer, P.2
  • 12
    • 0033233496 scopus 로고    scopus 로고
    • On the role of the mean curvature in some singularly perturbed Neumann problems
    • [DeFW]
    • [DeFW] M. DEL PINO, P. FELMER, J. WEI, On the role of the mean curvature in some singularly perturbed Neumann problems, SIAM J. Math. Anal. 31 (1999), 63-79.
    • (1999) SIAM J. Math. Anal. , vol.31 , pp. 63-79
    • Del Pino, M.1    Felmer, P.2    Wei, J.3
  • 15
    • 0001613187 scopus 로고
    • Nonspreading wave packets for the cubic Schrodinger equation with a bounded potential
    • [FW]
    • [FW] A. FLOER, A. WEINSTEIN, Nonspreading wave packets for the cubic Schrodinger equation with a bounded potential, J. Funct. Anal. 69 (1986), 397-408.
    • (1986) J. Funct. Anal. , vol.69 , pp. 397-408
    • Floer, A.1    Weinstein, A.2
  • 16
    • 0015454185 scopus 로고
    • A theory of biological pattern formation
    • [GM]
    • [GM] A. GIERER, H. MEINHARDT, A theory of biological pattern formation, Kybernetik (Berlin) 12 (1972), 30-39.
    • (1972) Kybernetik (Berlin) , vol.12 , pp. 30-39
    • Gierer, A.1    Meinhardt, H.2
  • 17
    • 0003226251 scopus 로고    scopus 로고
    • Existence of multipeak solutions for a semilinear Neumann problem via nonsmooth critical point theory
    • [GrPW]
    • [GrPW] M. GROSSI, A. PISTOIA, J. WEI, Existence of multipeak solutions for a semilinear Neumann problem via nonsmooth critical point theory, Calc. Var. Partial Differential Equations 11:2 (2000), 143-175.
    • (2000) Calc. Var. Partial Differential Equations , vol.11 , Issue.2 , pp. 143-175
    • Grossi, M.1    Pistoia, A.2    Wei, J.3
  • 18
    • 0000860177 scopus 로고    scopus 로고
    • Multipeak solutions for a semilinear Neumann problem
    • [Gu]
    • [Gu] C. GUI, Multipeak solutions for a semilinear Neumann problem, Duke Math. J. 84 (1996), 739-769.
    • (1996) Duke Math. J. , vol.84 , pp. 739-769
    • Gui, C.1
  • 19
    • 0034380572 scopus 로고    scopus 로고
    • On multiple mixed interior and boundary peak solutions for some singularly perturbed Neumann problems
    • [GuW]
    • [GuW] C. GUI, J. WEI, On multiple mixed interior and boundary peak solutions for some singularly perturbed Neumann problems, Canad. J. Math. 52:3 (2000), 522-538.
    • (2000) Canad. J. Math. , vol.52 , Issue.3 , pp. 522-538
    • Gui, C.1    Wei, J.2
  • 20
    • 0002025752 scopus 로고    scopus 로고
    • Multiple boundary peak solutions for some singularly perturbed Neumann problems
    • [GuWW]
    • [GuWW] C. GUI, J. WEI, M. WINTER., Multiple boundary peak solutions for some singularly perturbed Neumann problems, Ann. Inst. H. Poincaré Anal. Non Linéaire 17:1 (2000), 47-82.
    • (2000) Ann. Inst. H. Poincaré Anal. Non Linéaire , vol.17 , Issue.1 , pp. 47-82
    • Gui, C.1    Wei, J.2    Winter, M.3
  • 21
    • 0039531750 scopus 로고
    • Perturbation Theory for Linear Operators, Second edition
    • [K] SpringerVerlag, Berlin-New York
    • [K] T. KATO, Perturbation Theory for Linear Operators, Second edition, Grundlehren der Mathematischen Wissenschaften, Band 132. SpringerVerlag, Berlin-New York, 1976.
    • (1976) Grundlehren der Mathematischen Wissenschaften , vol.132
    • Kato, T.1
  • 24
    • 0000984635 scopus 로고    scopus 로고
    • On a singularly perturbed equation with Neumann boundary conditions
    • [L]
    • [L] Y.Y. Li, On a singularly perturbed equation with Neumann boundary conditions, Comm. Partial Differential Equations 23 (1998), 487-545.
    • (1998) Comm. Partial Differential Equations , vol.23 , pp. 487-545
    • Li, Y.Y.1
  • 25
    • 0032348339 scopus 로고    scopus 로고
    • The Dirichlet problem for singularly perturbed elliptic equations
    • [LN]
    • [LN] Y.Y. Li, L. NIRENBERG, The Dirichlet problem for singularly perturbed elliptic equations, Comm. Pure Appl. Math. 51 (1998), 1445-1490.
    • (1998) Comm. Pure Appl. Math. , vol.51 , pp. 1445-1490
    • Li, Y.Y.1    Nirenberg, L.2
  • 26
    • 0002542873 scopus 로고
    • Large amplitude stationary solutions to a chemotaxis systems
    • [LiNT]
    • [LiNT] C.-S. LIN, W.-M. Ni, I. TAKAGI, Large amplitude stationary solutions to a chemotaxis systems, J. Differential Equations 72 (1988), 1-27.
    • (1988) J. Differential Equations , vol.72 , pp. 1-27
    • Lin, C.-S.1    Ni, W.-M.2    Takagi, I.3
  • 28
    • 0036425683 scopus 로고    scopus 로고
    • Boundary concentration phenomena for a singularly perturbed elliptic problem
    • [MM1]
    • [MM1] A. MALCHIODI, M. MONTENEGRO, Boundary concentration phenomena for a singularly perturbed elliptic problem, Comm. Pure Appl. Math, 15 (2002), 1507-1568.
    • (2002) Comm. Pure Appl. Math , vol.15 , pp. 1507-1568
    • Malchiodi, A.1    Montenegro, M.2
  • 29
    • 4043167077 scopus 로고    scopus 로고
    • Multidimensional Boundary-layers for a singularly perturbed Neumann problem
    • [MM2]
    • [MM2] A. MALCHIODI, M. MONTENEGRO, Multidimensional Boundary-layers for a singularly perturbed Neumann problem, Duke Math. J. 124:1 (2004), 105-143.
    • (2004) Duke Math. J. , vol.124 , Issue.1 , pp. 105-143
    • Malchiodi, A.1    Montenegro, M.2
  • 30
    • 13844306817 scopus 로고    scopus 로고
    • Multiple clustered layer solutions for semilinear neumann problems on a ball
    • [MNW]
    • [MNW] A. MALCHIODI, W.M. Ni, J. WEI, Multiple clustered layer solutions for semilinear neumann problems on a ball, Ann. I.H.P. AN 22 (2005), 143-163.
    • (2005) Ann. I.H.P. AN , vol.22 , pp. 143-163
    • Malchiodi, A.1    Ni, W.M.2    Wei, J.3
  • 31
    • 33748998848 scopus 로고    scopus 로고
    • Foliations by constant mean curvature tubes
    • [MaP] to appear
    • [MaP] R. MAZZEO, F. PACARD, Foliations by constant mean curvature tubes, Comm. Anal. Geom., to appear.
    • Comm. Anal. Geom.
    • Mazzeo, R.1    Pacard, F.2
  • 32
    • 0003002827 scopus 로고    scopus 로고
    • Diffusion, cross-diffusion, and their spike-layer steady states
    • [N]
    • [N] W.M. Ni, Diffusion, cross-diffusion, and their spike-layer steady states, Notices Amer. Math. Soc. 45:1 (1998), 9-18.
    • (1998) Notices Amer. Math. Soc. , vol.45 , Issue.1 , pp. 9-18
    • Ni, W.M.1
  • 33
    • 84990581933 scopus 로고
    • On the shape of least-energy solution to a semilinear Neumann problem
    • [NT1]
    • [NT1] W.M. Ni, I. TAKAGI, On the shape of least-energy solution to a semilinear Neumann problem, Comm. Pure Appl. Math., 41 (1991), 819-851.
    • (1991) Comm. Pure Appl. Math. , vol.41 , pp. 819-851
    • Ni, W.M.1    Takagi, I.2
  • 34
    • 84971179248 scopus 로고
    • Locating the peaks of least-energy solutions to a semilinear Neumann problem
    • [NT2]
    • [NT2] W.M. Ni, I. TAKAGI, Locating the peaks of least-energy solutions to a semilinear Neumann problem, Duke Math. J. 70, (1993), 247-281.
    • (1993) Duke Math. J. , vol.70 , pp. 247-281
    • Ni, W.M.1    Takagi, I.2
  • 35
    • 0038506579 scopus 로고    scopus 로고
    • Stability of least energy patterns of the shadow system for an activator-inhibitor model. Recent topics in mathematics moving toward science and engineering
    • [NTY]
    • [NTY] W.M. Ni, I. TAKAGI, E. YANAGIDA, Stability of least energy patterns of the shadow system for an activator-inhibitor model. Recent topics in mathematics moving toward science and engineering, Japan J. Indust. Appl. Math. 18:2 (2001), 259-272.
    • (2001) Japan J. Indust. Appl. Math. , vol.18 , Issue.2 , pp. 259-272
    • Ni, W.M.1    Takagi, I.2    Yanagida, E.3
  • 36
    • 0000998584 scopus 로고
    • On positive mupltibum states of nonlinear Schroedinger equation under multpile well potentials
    • [O]
    • [O] Y.-G. OH, On positive mupltibum states of nonlinear Schroedinger equation under multpile well potentials, Comm. Math. Phys. 131 (1990), 223-253.
    • (1990) Comm. Math. Phys. , vol.131 , pp. 223-253
    • Oh, Y.-G.1
  • 37
    • 0037059109 scopus 로고    scopus 로고
    • Periodic solutions for Hamiltonian systems under strong constraining forces
    • [SZ]
    • [SZ] J. SHATAH, C. ZENG, Periodic solutions for Hamiltonian systems under strong constraining forces, J. Differential Equations 186:2 (2002), 572-585.
    • (2002) J. Differential Equations , vol.186 , Issue.2 , pp. 572-585
    • Shatah, J.1    Zeng, C.2
  • 38
    • 0036701115 scopus 로고    scopus 로고
    • Semilinear Neumann boundary value problems on a rectangle
    • [Sh]
    • [Sh] J. SHI, Semilinear Neumann boundary value problems on a rectangle, Trans. Amer. Math. Soc. 354:8 (2002), 3117-3154.
    • (2002) Trans. Amer. Math. Soc. , vol.354 , Issue.8 , pp. 3117-3154
    • Shi, J.1
  • 40
    • 21144478287 scopus 로고
    • On the existence of multiple, single-peaked solutions for a semilinear Neumann problem
    • [W]
    • [W] Z.-Q. WANG, On the existence of multiple, single-peaked solutions for a semilinear Neumann problem, Arch. Rational Mech. Anal. 120 (1992), 375-399.
    • (1992) Arch. Rational Mech. Anal. , vol.120 , pp. 375-399
    • Wang, Z.-Q.1
  • 41
    • 0030578649 scopus 로고    scopus 로고
    • On the construction of single-peaked solutions to a singularly perturbed semilinear Dirichlet problem
    • [We1]
    • [We1] J. WEI, On the construction of single-peaked solutions to a singularly perturbed semilinear Dirichlet problem, J. Differential Equations 129 (1996), 315-333.
    • (1996) J. Differential Equations , vol.129 , pp. 315-333
    • Wei, J.1
  • 42
    • 0031562011 scopus 로고    scopus 로고
    • On the boundary spike layer solutions of a singularly perturbed semilinear Neumann problem
    • [We2]
    • [We2] J. WEI, On the boundary spike layer solutions of a singularly perturbed semilinear Neumann problem, J. Differential Equations 134 (1997), 104-133.
    • (1997) J. Differential Equations , vol.134 , pp. 104-133
    • Wei, J.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.