메뉴 건너뛰기




Volumn 222, Issue 6, 2009, Pages 2173-2195

A Bahri-Lions theorem revisited

Author keywords

Biharmonic operator; Elliptic systems; Perturbation from symmetry; Semilinear elliptic equations; Sign changing solutions; Variational methods

Indexed keywords


EID: 70349559696     PISSN: 00018708     EISSN: 10902082     Source Type: Journal    
DOI: 10.1016/j.aim.2009.07.013     Document Type: Article
Times cited : (26)

References (42)
  • 1
    • 0033465124 scopus 로고    scopus 로고
    • A superquadratic indefinite elliptic system and its Morse-Conley-Floer homology
    • Angenent S., and van der Vorst R. A superquadratic indefinite elliptic system and its Morse-Conley-Floer homology. Math. Z. 231 (1999) 203-248
    • (1999) Math. Z. , vol.231 , pp. 203-248
    • Angenent, S.1    van der Vorst, R.2
  • 2
    • 0012370640 scopus 로고
    • Topological results on a certain class of functionals and applications
    • Bahri A. Topological results on a certain class of functionals and applications. J. Funct. Anal. 41 (1981) 397-427
    • (1981) J. Funct. Anal. , vol.41 , pp. 397-427
    • Bahri, A.1
  • 3
    • 84968503357 scopus 로고
    • A perturbation method in critical point theory and applications
    • Bahri A., and Berestycki H. A perturbation method in critical point theory and applications. Trans. Amer. Math. Soc. 267 (1981) 1-32
    • (1981) Trans. Amer. Math. Soc. , vol.267 , pp. 1-32
    • Bahri, A.1    Berestycki, H.2
  • 4
    • 84990591594 scopus 로고
    • Morse-index of some min-max critical points. I. Application to multiplicity results
    • Bahri A., and Lions P.L. Morse-index of some min-max critical points. I. Application to multiplicity results. Comm. Pure Appl. Math. 41 (1988) 1027-1037
    • (1988) Comm. Pure Appl. Math. , vol.41 , pp. 1027-1037
    • Bahri, A.1    Lions, P.L.2
  • 5
    • 0035922965 scopus 로고    scopus 로고
    • Critical point theory on partially ordered Hilbert spaces
    • Bartsch T. Critical point theory on partially ordered Hilbert spaces. J. Funct. Anal. 186 (2001) 117-152
    • (2001) J. Funct. Anal. , vol.186 , pp. 117-152
    • Bartsch, T.1
  • 6
    • 0034400761 scopus 로고    scopus 로고
    • On the Morse indices of sign-changing solutions for nonlinear elliptic problems
    • Bartsch T., Chang K.C., and Wang Z.-Q. On the Morse indices of sign-changing solutions for nonlinear elliptic problems. Math. Z. 233 (2000) 655-677
    • (2000) Math. Z. , vol.233 , pp. 655-677
    • Bartsch, T.1    Chang, K.C.2    Wang, Z.-Q.3
  • 7
    • 1642345034 scopus 로고    scopus 로고
    • Sign changing solutions of superlinear Schrödinger equations
    • Bartsch T., Liu Z., and Weth T. Sign changing solutions of superlinear Schrödinger equations. Comm. Partial Differential Equations 29 (2004) 25-42
    • (2004) Comm. Partial Differential Equations , vol.29 , pp. 25-42
    • Bartsch, T.1    Liu, Z.2    Weth, T.3
  • 8
    • 38749140170 scopus 로고    scopus 로고
    • The Dirichlet problem for superlinear elliptic equations
    • Stationary Partial Differential Equations. Chipot M., and Quittner P. (Eds), Elsevier
    • Bartsch T., Wang Z.-Q., and Willem M. The Dirichlet problem for superlinear elliptic equations. In: Chipot M., and Quittner P. (Eds). Stationary Partial Differential Equations. Handb. Differ. Equ. vol. 2 (2005), Elsevier 1-55
    • (2005) Handb. Differ. Equ. , vol.2 , pp. 1-55
    • Bartsch, T.1    Wang, Z.-Q.2    Willem, M.3
  • 9
    • 1642367059 scopus 로고    scopus 로고
    • A note on additional properties of sign changing solutions to superlinear elliptic equations
    • Bartsch T., and Weth T. A note on additional properties of sign changing solutions to superlinear elliptic equations. Topol. Methods Nonlinear Anal. 22 (2003) 1-14
    • (2003) Topol. Methods Nonlinear Anal. , vol.22 , pp. 1-14
    • Bartsch, T.1    Weth, T.2
  • 10
    • 0034347258 scopus 로고    scopus 로고
    • The multiplicity of solutions in non-homogeneous boundary value problems
    • Bolle P., Ghoussoub N., and Tehrani H. The multiplicity of solutions in non-homogeneous boundary value problems. Manuscripta Math. 101 (2000) 325-350
    • (2000) Manuscripta Math. , vol.101 , pp. 325-350
    • Bolle, P.1    Ghoussoub, N.2    Tehrani, H.3
  • 11
    • 61549091226 scopus 로고    scopus 로고
    • Multiple critical points of perturbed symmetric strongly indefinite functionals
    • Erratum:
    • Bonheure D., and Ramos M. Multiple critical points of perturbed symmetric strongly indefinite functionals. Ann. Inst. H. Poincaré Anal. Non Linéaire 26 (2009) 675-688 Erratum:
    • (2009) Ann. Inst. H. Poincaré Anal. Non Linéaire , vol.26 , pp. 675-688
    • Bonheure, D.1    Ramos, M.2
  • 12
    • 65549150723 scopus 로고    scopus 로고
    • Multiple critical points of perturbed symmetric strongly indefinite functionals
    • Bonheure D., and Ramos M. Multiple critical points of perturbed symmetric strongly indefinite functionals. Ann. Inst. H. Poincaré Anal. Non Linéaire 26 (2009) 1049-1054
    • (2009) Ann. Inst. H. Poincaré Anal. Non Linéaire , vol.26 , pp. 1049-1054
    • Bonheure, D.1    Ramos, M.2
  • 13
    • 0037408467 scopus 로고    scopus 로고
    • Some applications of a perturbative method to elliptic equations with non-homogeneous boundary conditions
    • Candela A.M., and Salvatore A. Some applications of a perturbative method to elliptic equations with non-homogeneous boundary conditions. Nonlinear Anal. 53 (2003) 299-317
    • (2003) Nonlinear Anal. , vol.53 , pp. 299-317
    • Candela, A.M.1    Salvatore, A.2
  • 14
    • 31144441674 scopus 로고    scopus 로고
    • Upper estimates for the energy of solutions of nonhomogeneous boundary value problems
    • Castro A., and Clapp M. Upper estimates for the energy of solutions of nonhomogeneous boundary value problems. Proc. Amer. Math. Soc. 134 (2006) 167-175
    • (2006) Proc. Amer. Math. Soc. , vol.134 , pp. 167-175
    • Castro, A.1    Clapp, M.2
  • 15
    • 0036002260 scopus 로고    scopus 로고
    • Deformation from symmetry and multiplicity of solutions in non-homogeneous problems
    • Chambers C., and Ghoussoub N. Deformation from symmetry and multiplicity of solutions in non-homogeneous problems. Discrete Contin. Dyn. Syst. 8 (2002) 267-281
    • (2002) Discrete Contin. Dyn. Syst. , vol.8 , pp. 267-281
    • Chambers, C.1    Ghoussoub, N.2
  • 16
    • 0002819535 scopus 로고
    • Infinite Dimensional Morse Theory and Multiple Solution Problems
    • Birkhäuser, Boston, MA
    • Chang K.C. Infinite Dimensional Morse Theory and Multiple Solution Problems. Progr. Nonlinear Differential Equations Appl. vol. 6 (1993), Birkhäuser, Boston, MA
    • (1993) Progr. Nonlinear Differential Equations Appl. , vol.6
    • Chang, K.C.1
  • 18
    • 0347748231 scopus 로고    scopus 로고
    • On the existence of many solutions for a class of superlinear elliptic systems
    • Conti M., Merizzi L., and Terracini S. On the existence of many solutions for a class of superlinear elliptic systems. J. Differential Equations 167 (2000) 357-387
    • (2000) J. Differential Equations , vol.167 , pp. 357-387
    • Conti, M.1    Merizzi, L.2    Terracini, S.3
  • 19
    • 0001891854 scopus 로고
    • Weak type estimates for singular values and the number of bound states of Schrödinger operators
    • Cwikel M. Weak type estimates for singular values and the number of bound states of Schrödinger operators. Ann. of Math. 106 (1977) 93-100
    • (1977) Ann. of Math. , vol.106 , pp. 93-100
    • Cwikel, M.1
  • 20
  • 21
    • 0000302191 scopus 로고
    • Nontrivial solutions of operator equations and Morse indices of critical points of min-max type
    • Lazer A.C., and Solimini S. Nontrivial solutions of operator equations and Morse indices of critical points of min-max type. Nonlinear Anal. 12 (1988) 761-775
    • (1988) Nonlinear Anal. , vol.12 , pp. 761-775
    • Lazer, A.C.1    Solimini, S.2
  • 22
    • 0036702017 scopus 로고    scopus 로고
    • Ljusternik-Schnirelmann theory in partially ordered Hilbert spaces
    • Li S., and Wang Z.-Q. Ljusternik-Schnirelmann theory in partially ordered Hilbert spaces. Trans. Amer. Math. Soc. 354 (2002) 3207-3227
    • (2002) Trans. Amer. Math. Soc. , vol.354 , pp. 3207-3227
    • Li, S.1    Wang, Z.-Q.2
  • 23
    • 84966224507 scopus 로고
    • Bounds on the eigenvalues of the Laplace and Schrödinger operators
    • Lieb E.H. Bounds on the eigenvalues of the Laplace and Schrödinger operators. Bull. Amer. Math. Soc. 82 (1976) 751-753
    • (1976) Bull. Amer. Math. Soc. , vol.82 , pp. 751-753
    • Lieb, E.H.1
  • 24
    • 0001000911 scopus 로고
    • Multiple solutions of perturbed superquadratic second order Hamiltonian systems
    • Long Y. Multiple solutions of perturbed superquadratic second order Hamiltonian systems. Trans. Amer. Math. Soc. 311 (1989) 749-780
    • (1989) Trans. Amer. Math. Soc. , vol.311 , pp. 749-780
    • Long, Y.1
  • 25
    • 21344490620 scopus 로고
    • Periodic solutions to some problems of n-body type
    • Majer P., and Terracini S. Periodic solutions to some problems of n-body type. Arch. Ration. Mech. Anal. 124 (1993) 381-404
    • (1993) Arch. Ration. Mech. Anal. , vol.124 , pp. 381-404
    • Majer, P.1    Terracini, S.2
  • 26
    • 34748907866 scopus 로고    scopus 로고
    • Singularity and decay estimates in superlinear problems via Liouville-type theorems. Part I: Elliptic equations and systems
    • Poláçik P., Quittner P., and Souplet P. Singularity and decay estimates in superlinear problems via Liouville-type theorems. Part I: Elliptic equations and systems. Duke Math. J. 139 (2007) 555-579
    • (2007) Duke Math. J. , vol.139 , pp. 555-579
    • Poláçik, P.1    Quittner, P.2    Souplet, P.3
  • 27
    • 0000594598 scopus 로고
    • Multiple critical points of perturbed symmetric functionals
    • Rabinowitz P. Multiple critical points of perturbed symmetric functionals. Trans. Amer. Math. Soc. 272 (1982) 753-769
    • (1982) Trans. Amer. Math. Soc. , vol.272 , pp. 753-769
    • Rabinowitz, P.1
  • 28
    • 0001901435 scopus 로고
    • Minimax methods in critical point theory with applications to differential equations
    • Amer. Math. Soc., Providence, RI
    • Rabinowitz P. Minimax methods in critical point theory with applications to differential equations. CBMS Reg. Conf. Ser. Math. vol. 65 (1986), Amer. Math. Soc., Providence, RI
    • (1986) CBMS Reg. Conf. Ser. Math. , vol.65
    • Rabinowitz, P.1
  • 29
    • 51249166153 scopus 로고
    • Homotopical linking and Morse index estimates in min-max theorems
    • Ramos M., and Sanchez L. Homotopical linking and Morse index estimates in min-max theorems. Manuscripta Math. 87 (1995) 269-284
    • (1995) Manuscripta Math. , vol.87 , pp. 269-284
    • Ramos, M.1    Sanchez, L.2
  • 30
  • 31
    • 60449102619 scopus 로고    scopus 로고
    • Perturbation from symmetry for indefinite semilinear elliptic equations
    • Ramos M., and Tehrani H. Perturbation from symmetry for indefinite semilinear elliptic equations. Manuscripta Math. 128 (2009) 297-314
    • (2009) Manuscripta Math. , vol.128 , pp. 297-314
    • Ramos, M.1    Tehrani, H.2
  • 32
    • 0000359861 scopus 로고
    • The distribution of the discrete spectrum for singular differential operators
    • translation from
    • Rosenbljum G. The distribution of the discrete spectrum for singular differential operators. J. Sov. Math. Dokl. 13 (1972) 245-249 translation from
    • (1972) J. Sov. Math. Dokl. , vol.13 , pp. 245-249
    • Rosenbljum, G.1
  • 33
    • 0000424726 scopus 로고
    • The distribution of the discrete spectrum for singular differential operators
    • Rosenbljum G. The distribution of the discrete spectrum for singular differential operators. Dokl. Akad. Nauk SSSR 202 (1972) 1012-1015
    • (1972) Dokl. Akad. Nauk SSSR , vol.202 , pp. 1012-1015
    • Rosenbljum, G.1
  • 34
    • 26944458107 scopus 로고    scopus 로고
    • Infinitely many solutions to perturbed elliptic equations
    • Schechter M., and Zou W. Infinitely many solutions to perturbed elliptic equations. J. Funct. Anal. 228 (2005) 1-38
    • (2005) J. Funct. Anal. , vol.228 , pp. 1-38
    • Schechter, M.1    Zou, W.2
  • 36
    • 0001350959 scopus 로고
    • Morse index estimates in minimax theorems
    • Solimini S. Morse index estimates in minimax theorems. Manuscripta Math. 63 (1989) 421-453
    • (1989) Manuscripta Math. , vol.63 , pp. 421-453
    • Solimini, S.1
  • 37
    • 0000538563 scopus 로고
    • Infinitely many critical points for functionals which are not even and applications to superlinear boundary value problems
    • Struwe M. Infinitely many critical points for functionals which are not even and applications to superlinear boundary value problems. Manuscripta Math. 32 (1980) 335-364
    • (1980) Manuscripta Math. , vol.32 , pp. 335-364
    • Struwe, M.1
  • 39
    • 84954662413 scopus 로고
    • Morse indices at critical points related to the symmetric mountain pass theorem and applications
    • Tanaka K. Morse indices at critical points related to the symmetric mountain pass theorem and applications. Comm. Partial Differential Equations 14 (1989) 99-128
    • (1989) Comm. Partial Differential Equations , vol.14 , pp. 99-128
    • Tanaka, K.1
  • 40
    • 0006066131 scopus 로고    scopus 로고
    • Infinitely many solutions for indefinite semilinear elliptic equations without symmetry
    • Tehrani H.T. Infinitely many solutions for indefinite semilinear elliptic equations without symmetry. Comm. Partial Differential Equations 21 (1996) 541-557
    • (1996) Comm. Partial Differential Equations , vol.21 , pp. 541-557
    • Tehrani, H.T.1
  • 41
    • 0000221068 scopus 로고
    • Indice de Morse des points critiques obtenus par minimax
    • Viterbo C. Indice de Morse des points critiques obtenus par minimax. Ann. Inst. H. Poincaré Anal. Non Linéaire 5 (1988) 221-225
    • (1988) Ann. Inst. H. Poincaré Anal. Non Linéaire , vol.5 , pp. 221-225
    • Viterbo, C.1
  • 42
    • 70349554934 scopus 로고    scopus 로고
    • Nodal solutions to superlinear biharmonic equations via decomposition in dual cones
    • Weth T. Nodal solutions to superlinear biharmonic equations via decomposition in dual cones. Topol. Methods Nonlinear Anal. 28 (2006) 33-52
    • (2006) Topol. Methods Nonlinear Anal. , vol.28 , pp. 33-52
    • Weth, T.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.