메뉴 건너뛰기




Volumn 36, Issue 9, 2011, Pages 1654-1682

Pointwise blow-up phenomena for a dirichlet problem

Author keywords

Blow up; Classification results; Morse index; Non degeneracy; Rozenblyum lieb cwikel inequality

Indexed keywords


EID: 80051695212     PISSN: 03605302     EISSN: 15324133     Source Type: Journal    
DOI: 10.1080/03605302.2011.574304     Document Type: Article
Times cited : (10)

References (47)
  • 2
    • 84990585703 scopus 로고
    • Solutions of superlinear elliptic equations and their Morse indices
    • Bahri, A., Lions, P.L. (1992). Solutions of superlinear elliptic equations and their Morse indices. Comm. Pure Appl. Math. 45:1205-1215.
    • (1992) Comm. Pure Appl. Math , vol.45 , pp. 1205-1215
    • Bahri, A.1    Lions, P.L.2
  • 3
    • 0002556198 scopus 로고
    • The effect of the domain topology on the number of positive solutions of nonlinear elliptic problems
    • Benci, V., Cerami, G. (1991). The effect of the domain topology on the number of positive solutions of nonlinear elliptic problems. Arch. Rational Mech. Anal. 114:79-93.
    • (1991) Arch. Rational Mech. Anal , vol.114 , pp. 79-93
    • Benci, V.1    Cerami, G.2
  • 4
    • 0003160707 scopus 로고
    • Multiple positive solutions of some elliptic problems via the Morse theory and the domain topology
    • Benci, V., Cerami, G. (1994). Multiple positive solutions of some elliptic problems via the Morse theory and the domain topology. Calc. Var. Part. Diff. Eqs. 2:29-48.
    • (1994) Calc. Var. Part. Diff. Eqs , vol.2 , pp. 29-48
    • Benci, V.1    Cerami, G.2
  • 5
    • 0001067029 scopus 로고    scopus 로고
    • On the existence and profile of multi-peaked solutions to singularly perturbed semilinear Dirichlet problems
    • Cao, D., Dancer, E.N., Noussair, E., Yan, S. (1996). On the existence and profile of multi-peaked solutions to singularly perturbed semilinear Dirichlet problems. Discrete Contin. Dynam. Systems 2:221-236.
    • (1996) Discrete Contin. Dynam. Systems , vol.2 , pp. 221-236
    • Cao, D.1    Dancer, E.N.2    Noussair, E.3    Yan, S.4
  • 6
    • 0034692251 scopus 로고    scopus 로고
    • Multi-peak solutions for a singularly perturbed semilinear elliptic problem
    • Cao, D., Noussair, E. (2000). Multi-peak solutions for a singularly perturbed semilinear elliptic problem. J. Diff. Eqs. 166:266-289.
    • (2000) J. Diff. Eqs , vol.166 , pp. 266-289
    • Cao, D.1    Noussair, E.2
  • 7
    • 18144406711 scopus 로고    scopus 로고
    • Non existence of bounded-energy solutions for some semilinear elliptic equations with a large parameter
    • Castorina, D., Mancini, G. (2003). Non existence of bounded-energy solutions for some semilinear elliptic equations with a large parameter. Rend. Sem. Mat. Univ. Padova 110:147-160.
    • (2003) Rend. Sem. Mat. Univ. Padova , vol.110 , pp. 147-160
    • Castorina, D.1    Mancini, G.2
  • 8
    • 0001891854 scopus 로고
    • Weak type estimates for singular values and the number of bound states of Schrödinger operators
    • Cwikel, M. (1977). Weak type estimates for singular values and the number of bound states of Schrödinger operators. Ann. Math. 106:93-100.
    • (1977) Ann. Math , vol.106 , pp. 93-100
    • Cwikel, M.1
  • 9
    • 84971725019 scopus 로고
    • Some notes on the method of moving planes
    • Dancer, E.N. (1992). Some notes on the method of moving planes. Bull. Austral. Math. Soc. 46:425-434.
    • (1992) Bull. Austral. Math. Soc , vol.46 , pp. 425-434
    • Dancer, E.N.1
  • 10
    • 14844289582 scopus 로고    scopus 로고
    • n or on bounded domains with small diffusion
    • n or on bounded domains with small diffusion. Trans. Amer. Math. Soc. 357:1225-1243.
    • (2005) Trans. Amer. Math. Soc , vol.357 , pp. 1225-1243
    • Dancer, E.N.1
  • 11
    • 2142781601 scopus 로고    scopus 로고
    • n or on bounded domains with small diffusion
    • n or on bounded domains with small diffusion. II. Indiana Univ. Math. J. 53:97-108.
    • (2004) II. Indiana Univ. Math. J , vol.53 , pp. 97-108
    • Dancer, E.N.1
  • 12
    • 74549160615 scopus 로고    scopus 로고
    • On the classification of solutions of N: Stability outside a compact set and applications
    • Dancer, E.N., Farina, A. (2009). On the classification of solutions of N: Stability outside a compact set and applications. Proc. Amer. Math. Soc. 137:1333-1338.
    • (2009) Proc. Amer. Math. Soc , vol.137 , pp. 1333-1338
    • Dancer, E.N.1    Farina, A.2
  • 13
    • 0001076510 scopus 로고    scopus 로고
    • On the effect of domain topology in a singular perturbation problem
    • Dancer, E.N., Wei, J. (1998). On the effect of domain topology in a singular perturbation problem. Topol. Methods Nonlinear Anal. 11:227-248.
    • (1998) Topol. Methods Nonlinear Anal , vol.11 , pp. 227-248
    • Dancer, E.N.1    Wei, J.2
  • 14
    • 0001561236 scopus 로고    scopus 로고
    • A singularly perturbed elliptic problem in bounded domains with nontrivial topology
    • Dancer, E.N., Yan, S. (1999). A singularly perturbed elliptic problem in bounded domains with nontrivial topology. Adv. Diff. Eqs. 4:347-368.
    • (1999) Adv. Diff. Eqs , vol.4 , pp. 347-368
    • Dancer, E.N.1    Yan, S.2
  • 15
    • 0038160131 scopus 로고    scopus 로고
    • Effect of the domain geometry on the existence of multipeak solution for an elliptic problem
    • Dancer, E.N., Yan, S. (1999). Effect of the domain geometry on the existence of multipeak solution for an elliptic problem. Topol. Methods Nonlinear Anal. 14:1-38.
    • (1999) Topol. Methods Nonlinear Anal , vol.14 , pp. 1-38
    • Dancer, E.N.1    Yan, S.2
  • 16
    • 0041029478 scopus 로고    scopus 로고
    • On the role of distance function in some singular perturbation problems
    • del Pino, M., Felmer, P., Wei, J. (2000). On the role of distance function in some singular perturbation problems. Comm. Part. Diff. Eqs. 25:155-177.
    • (2000) Comm. Part. Diff. Eqs , vol.25 , pp. 155-177
    • del Pino, M.1    Felmer, P.2    Wei, J.3
  • 17
    • 0038160126 scopus 로고    scopus 로고
    • Multi-peak solutions for some singular perturbation problems
    • del Pino, M., Felmer, P., Wei, J. (2000). Multi-peak solutions for some singular perturbation problems. Calc. Var. Part. Diff. Eqs. 10:119-134.
    • (2000) Calc. Var. Part. Diff. Eqs , vol.10 , pp. 119-134
    • del Pino, M.1    Felmer, P.2    Wei, J.3
  • 18
    • 53849142180 scopus 로고    scopus 로고
    • Linear instability of entire solutions for a class of non-autonomous elliptic equations
    • Esposito, P. (2008). Linear instability of entire solutions for a class of non-autonomous elliptic equations. Proc. Roy. Soc. Edinburgh Sect. A 138:1005-1018.
    • (2008) Proc. Roy. Soc. Edinburgh Sect. A , vol.138 , pp. 1005-1018
    • Esposito, P.1
  • 19
    • 36248990914 scopus 로고    scopus 로고
    • Compactness along the branch of semistable and unstable solutions for an elliptic problem with a singular nonlinearity
    • Esposito, P., Ghoussoub, N., Guo, Y. (2007). Compactness along the branch of semistable and unstable solutions for an elliptic problem with a singular nonlinearity. Comm. Pure Appl. Math. 60:1731-1768.
    • (2007) Comm. Pure Appl. Math , vol.60 , pp. 1731-1768
    • Esposito, P.1    Ghoussoub, N.2    Guo, Y.3
  • 20
    • 34250694233 scopus 로고    scopus 로고
    • Asymptotic behavior of radial solutions for a semilinear elliptic problem on an annulus through Morse index
    • Esposito, P., Mancini, G., Santra, S., Srikanth, P.N. (2007). Asymptotic behavior of radial solutions for a semilinear elliptic problem on an annulus through Morse index. J. Diff. Eqs. 239:1-15.
    • (2007) J. Diff. Eqs , vol.239 , pp. 1-15
    • Esposito, P.1    Mancini, G.2    Santra, S.3    Srikanth, P.N.4
  • 22
    • 84971139225 scopus 로고
    • Existence and non existence results for semilinear elliptic problems in unbounded domains
    • Esteban, M.J., Lions, P.L. (1982). Existence and non existence results for semilinear elliptic problems in unbounded domains. Proc. Roy. Soc. Edinburgh Sect. A 93:1-14.
    • (1982) Proc. Roy. Soc. Edinburgh Sect. A , vol.93 , pp. 1-14
    • Esteban, M.J.1    Lions, P.L.2
  • 24
    • 84980187204 scopus 로고
    • The structure of complete stable minimal surfaces in 3-manifolds of nonnegative scalar curvature
    • Fischer-Colbrie, D., Schoen, R. (1980). The structure of complete stable minimal surfaces in 3-manifolds of nonnegative scalar curvature. Comm. Pure Appl. Math. 33:199-211.
    • (1980) Comm. Pure Appl. Math , vol.33 , pp. 199-211
    • Fischer-Colbrie, D.1    Schoen, R.2
  • 26
    • 34250271532 scopus 로고
    • Symmetry and related properties via maximum principle
    • Gidas, B., Ni, W.M., Nirenberg, L. (1979). Symmetry and related properties via 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
  • 28
    • 84939873114 scopus 로고
    • A priori bounds for positive solutions of nonlinear elliptic equations
    • Gidas, B., Spruck, J. (1981). A priori bounds for positive solutions of nonlinear elliptic equations. Comm. Part. Diff. Eqs. 6:883-901.
    • (1981) Comm. Part. Diff. Eqs , vol.6 , pp. 883-901
    • Gidas, B.1    Spruck, J.2
  • 29
    • 0003304216 scopus 로고
    • Elliptic Partial Differential Equations of Second Order
    • New York: Springer-Verlag
    • Gilbarg, D., Trudinger, N.S. (1977). Elliptic Partial Differential Equations Of Second Order. Grundlehren der Mathematischen Wissenschaften, Vol. 224. New York: Springer-Verlag.
    • (1977) Grundlehren Der Mathematischen Wissenschaften , vol.224
    • Gilbarg, D.1    Trudinger, N.S.2
  • 30
    • 25644433488 scopus 로고    scopus 로고
    • A nondegeneracy result for a nonlinear elliptic equation
    • Grossi, M. (2005). A nondegeneracy result for a nonlinear elliptic equation. Nonlinear Diff. Eqs. Appl. 12:227-241.
    • (2005) Nonlinear Diff. Eqs. Appl , vol.12 , pp. 227-241
    • Grossi, M.1
  • 31
    • 0346776043 scopus 로고    scopus 로고
    • On the effect of critical points of distance function in superlinear elliptic problems
    • Grossi, M., Pistoia, A. (2000). On the effect of critical points of distance function in superlinear elliptic problems. Adv. Diff. Eqs. 5:1397-1420.
    • (2000) Adv. Diff. Eqs , vol.5 , pp. 1397-1420
    • Grossi, M.1    Pistoia, A.2
  • 32
    • 0002610597 scopus 로고    scopus 로고
    • Multiple interior peak solutions for some singularly perturbed Neumann problems
    • Gui, C., Wei, J. (1999). Multiple interior peak solutions for some singularly perturbed Neumann problems. J. Diff. Eqs. 158:1-27.
    • (1999) J. Diff. Eqs , vol.158 , pp. 1-27
    • Gui, C.1    Wei, J.2
  • 34
    • 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
  • 35
    • 84966224507 scopus 로고
    • Bounds on the eigenvalues of the Laplace and Schrödinger operators
    • Lieb, E. (1976). Bounds on the eigenvalues of the Laplace and Schrödinger operators. Bull. Amer. Math. Soc. 82:751-753.
    • (1976) Bull. Amer. Math. Soc , vol.82 , pp. 751-753
    • Lieb, E.1
  • 36
    • 84972514202 scopus 로고
    • Positive solutions of elliptic equations
    • Moss, W.F., Piepenbrink, J. (1978). Positive solutions of elliptic equations. Pacific J. Math. 75:219-226.
    • (1978) Pacific. J. Math , vol.75 , pp. 219-226
    • Moss, W.F.1    Piepenbrink, J.2
  • 37
    • 84990662413 scopus 로고
    • On the location and profile of spike-layer solutions to singularly perturbed semilinear Dirichlet problems
    • Ni, W.M., Wei, J. (1995). On the location and profile of spike-layer solutions to singularly perturbed semilinear Dirichlet problems. Comm. Pure Math. Appl. 48:731-768.
    • (1995) Comm. Pure Math. Appl , vol.48 , pp. 731-768
    • Ni, W.M.1    Wei, J.2
  • 40
    • 80051694133 scopus 로고    scopus 로고
    • The role of the distance function in some singular perturbation problem
    • Pistoia, A. (2001). The role of the distance function in some singular perturbation problem. Methods Appl. Anal. 8:301-319.
    • (2001) Methods Appl. Anal , vol.8 , pp. 301-319
    • Pistoia, A.1
  • 41
    • 0000514956 scopus 로고
    • Eigenfunctions of the equation = 0
    • Pohozaev, S.I. (1965). Eigenfunctions of the equation = 0. Soviet Math. Dokl. 5:1408-1411.
    • (1965) Soviet Math. Dokl , vol.5 , pp. 1408-1411
    • Pohozaev, S.I.1
  • 42
    • 5644298291 scopus 로고    scopus 로고
    • Domination of semigroups and estimates for eigenvalues
    • (in Russian); translation in St. Petersburg Math. J. 12:831-845
    • Rozenblyum, G. (2000). Domination of semigroups and estimates for eigenvalues. Algebra i Analiz 12:158-177 (in Russian); translation in St. Petersburg Math. J. 12:831-845.
    • (2000) Algebra i Analiz , vol.12 , pp. 158-177
    • Rozenblyum, G.1
  • 43
    • 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
  • 44
    • 0030578649 scopus 로고    scopus 로고
    • On the construction of single-peaked solutions of a singularly perturbed semilinear Dirichlet problem
    • Wei, J. (1996). On the construction of single-peaked solutions of a singularly perturbed semilinear Dirichlet problem. J. Diff. Eqs. 129:315-333.
    • (1996) J. Diff. Eqs , vol.129 , pp. 315-333
    • Wei, J.1
  • 45
    • 0347188202 scopus 로고    scopus 로고
    • On the interior spike solutions for some singular perturbation problems
    • Wei, J. (1998). On the interior spike solutions for some singular perturbation problems. Proc. Roy. Soc. Edinburgh Sect. A 128:849-874.
    • (1998) Proc. Roy. Soc. Edinburgh Sect. A , vol.128 , pp. 849-874
    • Wei, J.1
  • 46
    • 0033414750 scopus 로고    scopus 로고
    • On single interior spike solutions of the Gierer-Meinhardt system: Uniqueness and spectrum estimates
    • Wei, J. (1999). On single interior spike solutions of the Gierer-Meinhardt system: Uniqueness and spectrum estimates. European J. Appl. Math. 10:353-378.
    • (1999) European J. Appl. Math , vol.10 , pp. 353-378
    • Wei, J.1
  • 47
    • 6344223915 scopus 로고    scopus 로고
    • On the effect of the domain geometry in singular perturbation problems
    • Wei, J. (2000). On the effect of the domain geometry in singular perturbation problems. Diff. Int. Eqs. 13:15-45.
    • (2000) Diff. Int. Eqs , vol.13 , pp. 15-45
    • Wei, J.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.