메뉴 건너뛰기




Volumn 29, Issue 11-12, 2004, Pages 1877-1904

Existence of multi-bump standing waves with a critical frequency for nonlinear Schrödinger equations

Author keywords

Critical frequency; Nondegeneracy; Nonlinear Schrodinger equations; Standing waves

Indexed keywords


EID: 10844253774     PISSN: 03605302     EISSN: None     Source Type: Journal    
DOI: 10.1081/PDE-200040205     Document Type: Article
Times cited : (30)

References (36)
  • 2
    • 0040435197 scopus 로고    scopus 로고
    • Multiplicity results for some nonlinear Schrödinger equations with potentials
    • Ambrosetti, A., Malchiodi, A., Secchi, S. (2001). Multiplicity results for some nonlinear Schrödinger equations with potentials. Arch. Ration. Mech. Anal. 159:253-271.
    • (2001) Arch. Ration. Mech. Anal. , vol.159 , pp. 253-271
    • Ambrosetti, A.1    Malchiodi, A.2    Secchi, S.3
  • 3
    • 0036778772 scopus 로고    scopus 로고
    • Standing waves for nonlinear Schrödinger equations with a radial potential
    • Byeon, J. (2002). Standing waves for nonlinear Schrödinger equations with a radial potential. Nonlinear Anal. 50:1135-1151.
    • (2002) Nonlinear Anal. , vol.50 , pp. 1135-1151
    • Byeon, J.1
  • 4
    • 0036027321 scopus 로고    scopus 로고
    • Standing waves with a critical frequency for nonlinear Schrödinger equations
    • Byeon, J., Wang, Z.-Q. (2002). Standing waves with a critical frequency for nonlinear Schrödinger equations. Arch. Rat. Mech. Anal. 165:295-316.
    • (2002) Arch. Rat. Mech. Anal. , vol.165 , pp. 295-316
    • Byeon, J.1    Wang, Z.-Q.2
  • 5
    • 0142230503 scopus 로고    scopus 로고
    • Standing waves with a critical frequency for nonlinear Schrödinger equations, II
    • Byeon, J., Wang, Z.-Q. (2003). Standing waves with a critical frequency for nonlinear Schrödinger equations, II. Calculus of Variations PDE 18:207-219.
    • (2003) Calculus of Variations PDE , vol.18 , pp. 207-219
    • Byeon, J.1    Wang, Z.-Q.2
  • 6
    • 0001617997 scopus 로고
    • The effect of domain shape on the number of positive solutions of certain nonlinear equations
    • Dancer, E. N. (1988). The effect of domain shape on the number of positive solutions of certain nonlinear equations. J. Differential Equations 74:120-156.
    • (1988) J. Differential Equations , vol.74 , pp. 120-156
    • Dancer, E.N.1
  • 8
    • 0005602251 scopus 로고    scopus 로고
    • The effect of the graph topology on the existence of multipeak solutions for nonlinear Schrödinger equations
    • Dancer, E. N., Lam, K. Y., Yan, S. (1998). The effect of the graph topology on the existence of multipeak solutions for nonlinear Schrödinger equations. Abstr. Appl. Anal. 3:293-318.
    • (1998) Abstr. Appl. Anal. , vol.3 , pp. 293-318
    • Dancer, E.N.1    Lam, K.Y.2    Yan, S.3
  • 9
    • 0001341199 scopus 로고    scopus 로고
    • Local mountain passes for semilinear elliptic problems in unbounded domains
    • Del Pino, M., Felmer, P. L. (1996). Local mountain passes for semilinear elliptic problems in unbounded domains. Calculus of Variations PDE 4:121-137.
    • (1996) Calculus of Variations PDE , vol.4 , pp. 121-137
    • Del Pino, M.1    Felmer, P.L.2
  • 10
    • 0031237479 scopus 로고    scopus 로고
    • Semi-classical states for nonlinear Schrödinger equations
    • Del Pino, M., Felmer, P. L. (1997). Semi-classical states for nonlinear Schrödinger equations. J. Funct. Anal. 149:245-265.
    • (1997) J. Funct. Anal. , vol.149 , pp. 245-265
    • Del Pino, M.1    Felmer, P.L.2
  • 11
    • 0000260189 scopus 로고    scopus 로고
    • Multi-peak bound states for nonlinear Schrödinger equations
    • Del Pino, M., Felmer, P. L. (1998). Multi-peak bound states for nonlinear Schrödinger equations. Ann. Inst. Henri Poincaré 15:127-149.
    • (1998) Ann. Inst. Henri Poincaré , vol.15 , pp. 127-149
    • Del Pino, M.1    Felmer, P.L.2
  • 12
    • 0036026058 scopus 로고    scopus 로고
    • Semi-classical states of nonlinear Schrödinger equations: A variational reduction method
    • Del Pino, M., Felmer, P. L. (2002). Semi-classical states of nonlinear Schrödinger equations: A variational reduction method. Math. Ann. 324:1-32.
    • (2002) Math. Ann. , vol.324 , pp. 1-32
    • Del Pino, M.1    Felmer, P.L.2
  • 13
    • 0032345338 scopus 로고    scopus 로고
    • Existence of positive bound states of nonlinear Schrödinger equations with saddle-like potential
    • Del Pino, M., Felmer, P. L., Miyagaki, O. H. (1998). Existence of positive bound states of nonlinear Schrödinger equations with saddle-like potential. Nonlinear Anal. TMA 34:979-989.
    • (1998) Nonlinear Anal. TMA , vol.34 , pp. 979-989
    • Del Pino, M.1    Felmer, P.L.2    Miyagaki, O.H.3
  • 14
    • 0001613187 scopus 로고
    • Nonspreading wave packets for the cubic Schrödinger equations with a bounded potential
    • Floer, A., Weinstein, A. (1986). Nonspreading wave packets for the cubic Schrödinger equations with a bounded potential. J. Funct. Anal. 69:397-408.
    • (1986) J. Funct. Anal. , vol.69 , pp. 397-408
    • Floer, A.1    Weinstein, A.2
  • 15
    • 34250271532 scopus 로고
    • Symmetry and related properties via the maximum principle
    • Gidas, B., Ni, W. M., Nirenberg, L. (1979). Symmetry and related properties via the maximum principle. Comm. Math. Phys. 68:209-243.
    • (1979) Comm. Math. Phys. , vol.68 , pp. 209-243
    • Gidas, B.1    Ni, W.M.2    Nirenberg, L.3
  • 17
    • 0000616123 scopus 로고    scopus 로고
    • Existence of multi-bump solutions for nonlinear Schrödinger equations via variational method
    • Gui, C. (1996). Existence of multi-bump solutions for nonlinear Schrödinger equations via variational method. Comm. PDE 21:787-820.
    • (1996) Comm. PDE , vol.21 , pp. 787-820
    • Gui, C.1
  • 18
    • 0037137992 scopus 로고    scopus 로고
    • Structure of positive radial solutions to scalar field equations with harmonic potential
    • Hirose, M., Ohta, M. (2002). Structure of positive radial solutions to scalar field equations with harmonic potential. J. Differential Equations 178:519-540.
    • (2002) J. Differential Equations , vol.178 , pp. 519-540
    • Hirose, M.1    Ohta, M.2
  • 19
    • 0000825718 scopus 로고    scopus 로고
    • On interacting bumps of semi-classical states of nonlinear Schrödinger equations
    • Kang, X., Wei, J. (2000). On interacting bumps of semi-classical states of nonlinear Schrödinger equations. Adv. Differential Equations 5:899-928.
    • (2000) Adv. Differential Equations , vol.5 , pp. 899-928
    • Kang, X.1    Wei, J.2
  • 21
    • 0000264842 scopus 로고    scopus 로고
    • On a singularly perturbed elliptic equation
    • Li, Y. Y. (1997). On a singularly perturbed elliptic equation. Adv. Differential Equations. 2:955-980.
    • (1997) Adv. Differential Equations , vol.2 , pp. 955-980
    • Li, Y.Y.1
  • 22
    • 0000984635 scopus 로고    scopus 로고
    • On a singularly perturbed equation with Neumann boundary condition
    • Li, Y. Y. (1998). On a singularly perturbed equation with Neumann boundary condition. Comm. Partial Differential Equations 23:487-545.
    • (1998) Comm. Partial Differential Equations , vol.23 , pp. 487-545
    • Li, Y.Y.1
  • 23
    • 0032348339 scopus 로고    scopus 로고
    • The dirichlet problem for singularly perturbed elliptic equations
    • Li, Y. Y., Nirenberg, L. (1998). The Dirichlet problem for singularly perturbed elliptic equations. Comm. Pure Appl. Math. 51:1445-1490.
    • (1998) Comm. Pure Appl. Math. , vol.51 , pp. 1445-1490
    • Li, Y.Y.1    Nirenberg, L.2
  • 27
  • 29
    • 0000998584 scopus 로고
    • On positive multi-lump bound states of nonlinear Schrödinger equations under multiple well potential
    • Oh, Y. G. (1990). On positive multi-lump bound states of nonlinear Schrödinger equations under multiple well potential. Comm. Math. Phys. 131:223-253.
    • (1990) Comm. Math. Phys. , vol.131 , pp. 223-253
    • Oh, Y.G.1
  • 31
    • 34249835055 scopus 로고
    • On a class of nonlinear Schrödinger equations
    • Rabinowitz, P. H. (1992). On a class of nonlinear Schrödinger equations. Z. Angew. Math. Phys. 43:270-291.
    • (1992) Z. Angew. Math. Phys. , vol.43 , pp. 270-291
    • Rabinowitz, P.H.1
  • 33
    • 0000540347 scopus 로고
    • Existence of solitary waves in higher demensions
    • Strauss, W. (1977). Existence of solitary waves in higher demensions. Comm. Math. Phys. 55:149-162.
    • (1977) Comm. Math. Phys. , vol.55 , pp. 149-162
    • Strauss, W.1
  • 35
    • 34250081368 scopus 로고
    • On concentration of positive bound states of nonlinear Schrödinger equations
    • Wang, X. (1993). On concentration of positive bound states of nonlinear Schrödinger equations. Comm. Math. Phys. 153:229-244.
    • (1993) Comm. Math. Phys. , vol.153 , pp. 229-244
    • Wang, X.1
  • 36
    • 0033589578 scopus 로고    scopus 로고
    • Existence and symmetry of multi-bump solutions for nonlinear Schrödinger equations
    • Wang, Z.-Q. (1999). Existence and symmetry of multi-bump solutions for nonlinear Schrödinger equations. J. Differential Equations 159:102-137.
    • (1999) J. Differential Equations , vol.159 , pp. 102-137
    • Wang, Z.-Q.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.