메뉴 건너뛰기




Volumn 362, Issue 4, 2010, Pages 1981-2001

Singularly perturbed nonlinear dirichlet problems with a general nonlinearity

Author keywords

[No Author keywords available]

Indexed keywords


EID: 77950887105     PISSN: 00029947     EISSN: None     Source Type: Journal    
DOI: 10.1090/S0002-9947-09-04746-1     Document Type: Article
Times cited : (35)

References (27)
  • 1
    • 84968521876 scopus 로고
    • Symmetric decreasing rearrangement is sometimes continuous
    • MR1002633 (90f:49038)
    • F. j. almgren and e.h. LlEB, Symmetric decreasing rearrangement is sometimes continuous, J. Amer. Math. Soc., 2 (1989), 683-773. MR1002633 (90f:49038)
    • (1989) J. Amer. Math. Soc. , vol.2 , pp. 683-773
    • Almgren, F.J.1    Lleb, E.2
  • 2
    • 34548350707 scopus 로고
    • Dual variational methods in critical point theory and applications
    • MR0370183 (51:6412)
    • a. ambrosetti and p.h. rabinowitz, Dual variational methods in critical point theory and applications, J. Functional Analysis, 14 (1973), 349-381. MR0370183 (51:6412)
    • (1973) J. Functional Analysis , vol.14 , pp. 349-381
    • Ambrosetti, A.1    Rabinowitz, P.2
  • 3
    • 0000696702 scopus 로고    scopus 로고
    • Existence of large positive solutions of some nonlinear elliptic equations on singularly perturbed domains
    • j. Byeon, Existence of large positive solutions of some nonlinear elliptic equations on singularly perturbed domains, Comm. in Partial Differential Equations, 22 (1997), 1731-1769. MR1469588 (98i:35057) (Pubitemid 127357930)
    • (1997) Communications in Partial Differential Equations , vol.22 , Issue.9-10 , pp. 1731-1769
    • Byeon, J.1
  • 4
    • 26844542526 scopus 로고    scopus 로고
    • Mountain pass solutions for singularly perturbed nonlinear Dirichlet problems
    • DOI 10.1016/j.jde.2005.07.008, PII S0022039605002548
    • j. Byeon, Mountain pass solutions for singularly perturbed nonlinear Dirichlet problems, J. Differential Equations, 217 (2005), 257-281. MR2168823 (2006k:35081) (Pubitemid 41447731)
    • (2005) Journal of Differential Equations , vol.217 , Issue.2 , pp. 257-281
    • Byeon, J.1
  • 5
    • 34547328617 scopus 로고    scopus 로고
    • Standing waves for nonlinear Schrodinger equations with a general nonlinearity
    • MR2317788
    • j Byeon and l. jeanjean, Standing waves for nonlinear Schrodinger equations with a general nonlinearity, Arch. Rational Mech. Anal., 185 (2007), 185-200. MR2317788
    • (2007) Arch. Rational Mech. Anal. , vol.185 , pp. 185-200
    • Byeon, J.1    Jeanjean, L.2
  • 6
    • 36248941304 scopus 로고    scopus 로고
    • Multi-peak standing waves for nonlinear Schrodinger equations with a general nonlinearity
    • MR2335747
    • j Byeon and l. Jeanjean, Multi-peak standing waves for nonlinear Schrodinger equations with a general nonlinearity, Discrete Contin. Dyn. Syst., 19 (2007), 255-269. MR2335747
    • (2007) Discrete Contin. Dyn. Syst. , vol.19 , pp. 255-269
    • Byeon, J.1    Jeanjean, L.2
  • 7
    • 45849139773 scopus 로고    scopus 로고
    • Standing waves for nonlinear schrodinger equations with a general nonlinearity: One and two dimensional cases
    • MR2317788 (2009f:35071)
    • J Byeon, L. Jeanjean and K. Tanaka, Standing waves for nonlinear Schrodinger equations with a general nonlinearity: one and two dimensional cases, Comm. Partial Differential Equations, 33 (2008), 1113-1136. MR2317788 (2009f:35071)
    • (2008) Comm. Partial Differential Equations , vol.33 , pp. 1113-1136
    • Byeon, J.1    Jeanjean, L.2    Tanaka, K.3
  • 8
    • 0020591567 scopus 로고
    • NONLINEAR SCALAR FIELD EQUATIONS, I. EXISTENCE OF A GROUND STATE.
    • H. Berestycki, T. Gallouet and O. Kavian, Nonlinear Euclidean scalar field equations in the plane, C. R. Acad. Sci. Paris Ser. I Math., 297 (1983), 307-310. MR734575 (85e:35041) (Pubitemid 13555203)
    • (1983) Archive for Rational Mechanics and Analysis , vol.82 , Issue.4 , pp. 313-345
    • Berestycki, H.1    Lions, P.-L.2
  • 10
    • 0002131129 scopus 로고
    • Existence and multiplicity results for a semilinear elliptic eigenvalue problem
    • MR937538 (89j:35053)
    • p. clément and g. sweers, Existence and multiplicity results for a semilinear elliptic eigenvalue problem, Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4), 14 (1987), 97-121. MR937538 (89j:35053)
    • (1987) Ann. Scuola Norm. Sup. Pisa Cl. Sci. , vol.14 , Issue.4 , pp. 97-121
    • Clément, P.1    Sweers, G.2
  • 11
    • 18144414457 scopus 로고    scopus 로고
    • Some mountain-pass solutions for small diffusion
    • MR1989600 (2004e:35063)
    • E.N. DANCER, Some mountain-pass solutions for small diffusion, Differential Integral Equations, 16 (2003), 1013-1024. MR1989600 (2004e:35063)
    • (2003) Differential Integral Equations , vol.16 , pp. 1013-1024
    • Dancer, E.N.1
  • 12
    • 0001663580 scopus 로고    scopus 로고
    • Spike-layered solutions of singularly perturbed elliptic problems in a degenerate setting
    • MR1736974 (2001b:35027)
    • M. DEL Pino AND P.L. FELMER, Spike-layered solutions of singularly perturbed elliptic problems in a degenerate setting, Indiana Univ. Math. J., 48 (1999), 883-898. MR1736974 (2001b:35027)
    • (1999) Indiana Univ. Math. J. , vol.48 , pp. 883-898
    • Del Pino, M.1    Felmer, P.L.2
  • 13
    • 0041029478 scopus 로고    scopus 로고
    • On the role of distance function in some singular perturbation problems
    • MR1737546 (2000m:35017)
    • M. DEL PINO, P. FELMER AND J. WEI, On the role of distance function in some singular perturbation problems, Comm. Partial Differential Equations, 25 (2000), 155-177. MR1737546 (2000m:35017)
    • (2000) Comm. Partial Differential Equations , vol.25 , pp. 155-177
    • Delpino, M.1    Felmer, P.2    Wei, J.3
  • 14
    • 34250271532 scopus 로고
    • Symmetry and related properties via the maximum principle
    • MR544879 (80h:35043)
    • B. Gidas, W. N. Ni AND L. NIRENBERG, Symmetry and related properties via the maximum principle, Comm. Math. Phys., 68 (1979), 209-243. MR544879 (80h:35043)
    • (1979) Comm. Math. Phys. , vol.68 , pp. 209-243
    • Gidas, B.1    Ni, W.N.2    Nirenberg, L.3
  • 15
    • 84974488953 scopus 로고
    • The set of positive solutions of semilinear equations in large balls
    • MR877892 (88e:35063)
    • R. GARDNER AND L. A. PELETIER, The set of positive solutions of semilinear equations in large balls, Proc. Roy. Soc. Edinburgh Sect. A, 104 (1986), 53-72. MR877892 (88e:35063)
    • (1986) Proc. Roy. Soc. Edinburgh Sect. A , vol.104 , pp. 53-72
    • Gardner, R.1    Peletier, L.A.2
  • 16
    • 0003259059 scopus 로고
    • Elliptic partial differential equations of second order. Second edition
    • Springer, Berlin, MR737190 (86c:35035)
    • D. GILBARG AND N. S. TRUDINGER, Elliptic Partial Differential Equations of Second Order. Second edition, Grundlehren Math. Wiss. 224, Springer, Berlin, 1983. MR737190 (86c:35035)
    • (1983) Grundlehren Math. Wiss. , vol.224
    • Gilbarg, D.1    Trudinger, N.S.2
  • 17
    • 0000364966 scopus 로고
    • On spike solutions of singularly perturbed semilinear dirichlet problems
    • MR1303033 (95i:35099)
    • J. JANG, On spike solutions of singularly perturbed semilinear Dirichlet problems, J. Differential Equations, 114 (1994), 370-395. MR1303033 (95i:35099)
    • (1994) J. Differential Equations , vol.114 , pp. 370-395
    • Jang, J.1
  • 19
    • 0000296501 scopus 로고
    • Symetrie et compacite dans les espaces de sobolev
    • MR683027 (84k:46027)
    • P.L. LIONS, Symetrie et compacite dans les espaces de Sobolev, J. Funct. Anal., 49 (1982), 315-334. MR683027 (84k:46027)
    • (1982) J. Funct. Anal. , vol.49 , pp. 315-334
    • Lions, P.L.1
  • 20
    • 85030719142 scopus 로고
    • The concentration-compactness principle in the calculus of variations
    • MR778974 (87e:49035b)
    • P.L. LIONS, The concentration-compactness principle in the calculus of variations. The locally compact case. II. Ann. Inst. Henri Poincare, 1 (1984), 223-283. MR778974 (87e:49035b)
    • (1984) The Locally Compact Case. II. Ann. Inst. Henri Poincare , vol.1 , pp. 223-283
    • Lions, P.L.1
  • 21
    • 0032348339 scopus 로고    scopus 로고
    • The Dirichlet Problem for Singularly Perturbed Elliptic Equations
    • Y.Y. LI AND L. NIRENBERG, The Dirichlet problem for singularly perturbed elliptic equations, Comm. Pure Appl. Math., 51 (1998), 1445-1490. MR1639159 (99g:35014) (Pubitemid 128142131)
    • (1998) Communications on Pure and Applied Mathematics , vol.51 , Issue.11-12 , pp. 1445-1490
    • Li, Y.Y.1    Nirenberg, L.2
  • 22
    • 0000483708 scopus 로고    scopus 로고
    • On the location and profile of spike-layer solutions to a singularly perturbed semilinear Dirichlet problem: Intermediate solutions
    • W.M. NI, I. TAKAGI AND J. WEI, On the location and profile of spike-layer solutions to a singularly perturbed semilinear Dirichlet problem: intermediate solutions, Duke Math. J., 94 (1998), 597-618. MR1639546 (99h:35011) (Pubitemid 128379973)
    • (1998) Duke Mathematical Journal , vol.94 , Issue.3 , pp. 597-618
    • Ni, W.-M.1    Takagi, I.2    Wei, J.3
  • 23
    • 84990662413 scopus 로고
    • On the location and profile of spike-layer solutions to singularly perturbed semilinear Dirichlet problems
    • MR1342381 (96g:35077)
    • W.M. Ni AND J. WEI, On the location and profile of spike-layer solutions to singularly perturbed semilinear Dirichlet problems, Comm. Pure Appl. Math., 48 (1995), 731-768. MR1342381 (96g:35077)
    • (1995) Comm. Pure Appl. Math. , vol.48 , pp. 731-768
    • Ni, W.M.1    Wei, J.2
  • 24
    • 0002616111 scopus 로고    scopus 로고
    • The effect of the domain geometry in singular perturbation problems
    • E. NOUSSAIR AND S. Yan, The effect of the domain geometry in singular perturbation problems, Proc. London Math. Soc., 76 (1998), 427-452. MR1490244 (98m:35013) (Pubitemid 128737154)
    • (1998) Proceedings of the London Mathematical Society , vol.76 , Issue.2 , pp. 427-452
    • Noussair, E.S.1    Yan, S.2
  • 27
    • 0030578649 scopus 로고    scopus 로고
    • On the construction of single-peaked solutions to a singularly perturbed semilinear Dirichlet problem
    • DOI 10.1006/jdeq.1996.0120
    • J. Wei, On the construction of single-peaked solutions to a singularly perturbed semilinear Dirichlet problem, J. Differential Equations, 129 (1996), 315-333. MR1404386 (97f:35015) (Pubitemid 126165655)
    • (1996) Journal of Differential Equations , vol.129 , Issue.2 , pp. 315-333
    • Wei, J.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.