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Volumn 8, Issue 6, 2009, Pages 1779-1793

Low dimensional instability for semilinear and quasilinear problems in ℝN

Author keywords

Critical dimension; Linear instability; p Laplace operator

Indexed keywords


EID: 77249095229     PISSN: 15340392     EISSN: 15535258     Source Type: Journal    
DOI: 10.3934/cpaa.2009.8.1779     Document Type: Article
Times cited : (26)

References (33)
  • 1
    • 0347486747 scopus 로고    scopus 로고
    • 3 and a conjecture of De Giorgi, J. Amer. Math. Soc., 13 (2000), 725-739.
    • 3 and a conjecture of De Giorgi, J. Amer. Math. Soc., 13 (2000), 725-739.
  • 2
    • 84990585703 scopus 로고
    • Solutions of superlinear elliptic equations and their Morse indices
    • A. Bahri and P.-L. Lions, Solutions of superlinear elliptic equations and their Morse indices, Comm. Pure Appl. Math., 45 (1992), 1205-1215.
    • (1992) Comm. Pure Appl. Math , vol.45 , pp. 1205-1215
    • Bahri, A.1    Lions, P.-L.2
  • 4
    • 33746335682 scopus 로고    scopus 로고
    • Regularity of radial minimizers and extremal solutions of semilinear elliptic equations
    • X. Cabré and A. Capella, Regularity of radial minimizers and extremal solutions of semilinear elliptic equations, J. Funct. Anal., 238 (2006), 709-733.
    • (2006) J. Funct. Anal , vol.238 , pp. 709-733
    • Cabré, X.1    Capella, A.2
  • 5
    • 34248231815 scopus 로고    scopus 로고
    • Semi-stable and extremal solutions of reactions equations involving the p - Laplacian
    • X. Cabré and M. Sanchón, Semi-stable and extremal solutions of reactions equations involving the p - Laplacian, Commun. Pure Appl. Anal., 6 (2007), 43-67.
    • (2007) Commun. Pure Appl. Anal , vol.6 , pp. 43-67
    • Cabré, X.1    Sanchón, M.2
  • 7
    • 0016643640 scopus 로고
    • Some continuation and variational methods for positive solutions of nonlinear elliptic eigenvalue problems
    • M. G. Crandall and P. H. Rabinowitz, Some continuation and variational methods for positive solutions of nonlinear elliptic eigenvalue problems, Arch. Ration. Mech. Anal., 58 (1975), 207-218.
    • (1975) Arch. Ration. Mech. Anal , vol.58 , pp. 207-218
    • Crandall, M.G.1    Rabinowitz, P.H.2
  • 9
    • 5044226333 scopus 로고    scopus 로고
    • Regularity, monotonicity and symmetry of positive solutions of m-Laplace equations
    • L. Damascelli and B. Sciunzi, Regularity, monotonicity and symmetry of positive solutions of m-Laplace equations, J. Differential Equations, 206 (2004), 483-515.
    • (2004) J. Differential Equations , vol.206 , pp. 483-515
    • Damascelli, L.1    Sciunzi, B.2
  • 10
    • 33344470918 scopus 로고    scopus 로고
    • Harnack inequalities, maximum and comparison principles, and regularity of positive solutions of m-Laplace equations
    • L. Damascelli and B. Sciunzi, Harnack inequalities, maximum and comparison principles, and regularity of positive solutions of m-Laplace equations, Calc. Var. Partial Differential Equations, 25 (2006), 139-159.
    • (2006) Calc. Var. Partial Differential Equations , vol.25 , pp. 139-159
    • Damascelli, L.1    Sciunzi, B.2
  • 11
    • 37549032534 scopus 로고    scopus 로고
    • Finite Morse index solutions of exponential problems
    • E. N. Dancer, Finite Morse index solutions of exponential problems, Ann. Inst. H. Poincaré Anal. Non Linéaire, 25 (2008), 173-179.
    • (2008) Ann. Inst. H. Poincaré Anal. Non Linéaire , vol.25 , pp. 173-179
    • Dancer, E.N.1
  • 13
    • 77249091086 scopus 로고    scopus 로고
    • M. del Pino, M. Kowalczyk and J. Wei, On De Giorgi conjecture in dimensions N ≥ 9, preprint, arXiv:0806.3141.
    • M. del Pino, M. Kowalczyk and J. Wei, On De Giorgi conjecture in dimensions N ≥ 9, preprint, arXiv:0806.3141.
  • 14
    • 0001472514 scopus 로고
    • 1+α local regularity of weak solutions of degenerate elliptic equations
    • 1+α local regularity of weak solutions of degenerate elliptic equations, Nonlinear Anal., 7 (1983), 827-850.
    • (1983) Nonlinear Anal , vol.7 , pp. 827-850
    • Di Benedetto, E.1
  • 16
    • 44349087152 scopus 로고    scopus 로고
    • Compactness of a nonlinear eigenvalue problem with a singular nonlinearity
    • P. Esposito, Compactness of a nonlinear eigenvalue problem with a singular nonlinearity, Commun. Contemp. Math., 10 (2008), 17-45.
    • (2008) Commun. Contemp. Math , vol.10 , pp. 17-45
    • Esposito, P.1
  • 17
    • 53849142180 scopus 로고    scopus 로고
    • Linear instability of entire solutions for a class of non-autonomous elliptic equations
    • P. Esposito, Linear instability of entire solutions for a class of non-autonomous elliptic equations, Proc. Roy. Soc. Edinburgh Sect. A, 138 (2008), 1005-1018.
    • (2008) Proc. Roy. Soc. Edinburgh Sect. A , vol.138 , pp. 1005-1018
    • Esposito, P.1
  • 18
    • 36248990914 scopus 로고    scopus 로고
    • Compactness along the branch of semi-stable and unstable solutions for an elliptic problem with a singular nonlinearity
    • P. Esposito, N. Ghoussoub and Y. Guo, Compactness along the branch of semi-stable and unstable solutions for an elliptic problem with a singular nonlinearity, Comm. Pure Appl. Math., 60 (2007), 1731-1768.
    • (2007) Comm. Pure Appl. Math , vol.60 , pp. 1731-1768
    • Esposito, P.1    Ghoussoub, N.2    Guo, Y.3
  • 23
    • 0032373311 scopus 로고    scopus 로고
    • On a conjecture of De Giorgi and some related problems
    • N. Ghoussoub and C. Gui, On a conjecture of De Giorgi and some related problems, Math. Ann., 311 (1998), 481-491.
    • (1998) Math. Ann , vol.311 , pp. 481-491
    • Ghoussoub, N.1    Gui, C.2
  • 24
    • 34547676625 scopus 로고    scopus 로고
    • On the partial differential equations of electrostatic MEMS devices: Stationary case
    • N. Ghoussoub and Y. Guo, On the partial differential equations of electrostatic MEMS devices: stationary case, SIAM J. Math. Anal., 38 (2006/2007), 1423-1449.
    • (2006) SIAM J. Math. Anal , vol.38 , pp. 1423-1449
    • Ghoussoub, N.1    Guo, Y.2
  • 26
    • 0000405695 scopus 로고
    • Boundary regularity for solutions of degenerate elliptic equations
    • G.M. Lieberman, Boundary regularity for solutions of degenerate elliptic equations, Nonlinear Anal., 12 (1988), 1203-1219.
    • (1988) Nonlinear Anal , vol.12 , pp. 1203-1219
    • Lieberman, G.M.1
  • 27
    • 0034196168 scopus 로고    scopus 로고
    • Regularity of the extremal solution of semilinear elliptic equations
    • G. Nedev, Regularity of the extremal solution of semilinear elliptic equations, C. R. Math. Acad. Sci. Paris, 330 (2000), 997-1002.
    • (2000) C. R. Math. Acad. Sci. Paris , vol.330 , pp. 997-1002
    • Nedev, G.1
  • 28
    • 67249165287 scopus 로고    scopus 로고
    • Regularity of flat level sets in phase transitions
    • V. O. Savin, Regularity of flat level sets in phase transitions, Ann. of Math. (2), 169 (2009), 41-78.
    • (2009) Ann. of Math. (2) , vol.169 , pp. 41-78
    • Savin, V.O.1
  • 29
    • 33646346403 scopus 로고    scopus 로고
    • Flat level set regularity of p - Laplace phase transitions
    • vi+144 pp
    • V. O. Savin, B. Sciunzi and E. Valdinoci, Flat level set regularity of p - Laplace phase transitions, Mem. Amer. Math. Soc., 182 (2006), vi+144 pp.
    • (2006) Mem. Amer. Math. Soc , vol.182
    • Savin, V.O.1    Sciunzi, B.2    Valdinoci, E.3
  • 30
    • 0002260833 scopus 로고
    • Regularity of minimizing harmonic maps into the sphere
    • R. Schoen and K. Uhlenbeck, Regularity of minimizing harmonic maps into the sphere, Invent. Math., 78 (1984), 89-100.
    • (1984) Invent. Math , vol.78 , pp. 89-100
    • Schoen, R.1    Uhlenbeck, K.2
  • 31
    • 0002460686 scopus 로고
    • Minimal varieties in riemannian manifolds
    • J. Simons, Minimal varieties in riemannian manifolds, Ann. of Math., 88 (1968), 62-105.
    • (1968) Ann. of Math , vol.88 , pp. 62-105
    • Simons, J.1
  • 32
    • 33846445540 scopus 로고
    • Regularity for a more general class of quasilinear elliptic equations
    • P. Tolksdorf, Regularity for a more general class of quasilinear elliptic equations, J. Differential Equations, 51 (1984), 126-150.
    • (1984) J. Differential Equations , vol.51 , pp. 126-150
    • Tolksdorf, P.1
  • 33
    • 0036692518 scopus 로고    scopus 로고
    • Boundedness of the extremal solution for semilinear elliptic problems
    • D. Ye and F. Zhou, Boundedness of the extremal solution for semilinear elliptic problems, Commun. Contemp. Math., 4 (2002), 547-558.
    • (2002) Commun. Contemp. Math , vol.4 , pp. 547-558
    • Ye, D.1    Zhou, F.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.