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Volumn 247, Issue 11, 2009, Pages 3136-3162

Multiplicity of solutions for a fourth order problem with exponential nonlinearity

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EID: 70349205380     PISSN: 00220396     EISSN: 10902732     Source Type: Journal    
DOI: 10.1016/j.jde.2009.07.023     Document Type: Article
Times cited : (17)

References (39)
  • 1
    • 33748626787 scopus 로고    scopus 로고
    • Entire solutions for a semilinear fourth order elliptic problem with exponential nonlinearity
    • Arioli G., Gazzola F., and Grunau H.-C. Entire solutions for a semilinear fourth order elliptic problem with exponential nonlinearity. J. Differential Equations 230 2 (2006) 743-770
    • (2006) J. Differential Equations , vol.230 , Issue.2 , pp. 743-770
    • Arioli, G.1    Gazzola, F.2    Grunau, H.-C.3
  • 2
    • 17444378460 scopus 로고    scopus 로고
    • A semilinear fourth order elliptic problem with exponential nonlinearity
    • Arioli G., Gazzola F., Grunau H.-C., and Mitidieri E. A semilinear fourth order elliptic problem with exponential nonlinearity. SIAM J. Math. Anal. 36 4 (2005) 1226-1258
    • (2005) SIAM J. Math. Anal. , vol.36 , Issue.4 , pp. 1226-1258
    • Arioli, G.1    Gazzola, F.2    Grunau, H.-C.3    Mitidieri, E.4
  • 4
    • 0003329717 scopus 로고
    • Mathematical Problems from Combustion Theory
    • Springer-Verlag, New York
    • Bebernes J., and Eberly D. Mathematical Problems from Combustion Theory. Applied Mathematical Sciences vol. 83 (1989), Springer-Verlag, New York
    • (1989) Applied Mathematical Sciences , vol.83
    • Bebernes, J.1    Eberly, D.2
  • 5
    • 0000158596 scopus 로고
    • Equivalence and normal forms of germs of smooth mappings
    • 263
    • Belickiǐ G.R. Equivalence and normal forms of germs of smooth mappings. Uspekhi Mat. Nauk 33 1 (199) (1978) 95-155 263
    • (1978) Uspekhi Mat. Nauk , vol.33 , Issue.1 199 , pp. 95-155
    • Belickiǐ, G.R.1
  • 6
    • 70349193135 scopus 로고
    • Normal'nye Formy, Invarianty i Lokal'nye Otobrazheniya
    • Naukova Dumka, Kiev 173 pp. (in Russian)
    • Belickiǐ G.R. Normal'nye Formy, Invarianty i Lokal'nye Otobrazheniya. Normal Forms, Invariant and Local Mappings (1979), Naukova Dumka, Kiev 173 pp. (in Russian)
    • (1979) Normal Forms, Invariant and Local Mappings
    • Belickiǐ, G.R.1
  • 7
    • 17444403583 scopus 로고    scopus 로고
    • Some remarks on biharmonic elliptic problems with positive, increasing and convex nonlinearities
    • No. 34, 20 pp
    • Berchio E., and Gazzola F. Some remarks on biharmonic elliptic problems with positive, increasing and convex nonlinearities. Electron. J. Differential Equations (2005) No. 34, 20 pp
    • (2005) Electron. J. Differential Equations
    • Berchio, E.1    Gazzola, F.2
  • 8
    • 33746609428 scopus 로고    scopus 로고
    • Positivity preserving property for a class of biharmonic elliptic problems
    • Berchio E., Gazzola F., and Mitidieri E. Positivity preserving property for a class of biharmonic elliptic problems. J. Differential Equations 229 1 (2006) 1-23
    • (2006) J. Differential Equations , vol.229 , Issue.1 , pp. 1-23
    • Berchio, E.1    Gazzola, F.2    Mitidieri, E.3
  • 9
    • 0010950704 scopus 로고
    • Sur les équations intégrales non linéaires
    • Bratu G. Sur les équations intégrales non linéaires. Bull. Soc. Math. France 42 (1914) 113-142
    • (1914) Bull. Soc. Math. France , vol.42 , pp. 113-142
    • Bratu, G.1
  • 10
    • 70349208881 scopus 로고    scopus 로고
    • On a fourth order elliptic problem with a singular nonlinearity
    • Cassani D., do O J.M., and Ghoussoub N. On a fourth order elliptic problem with a singular nonlinearity. J. Adv. Nonlinear Stud. 9 (2009) 177-197
    • (2009) J. Adv. Nonlinear Stud. , vol.9 , pp. 177-197
    • Cassani, D.1    do O, J.M.2    Ghoussoub, N.3
  • 14
  • 15
    • 41449116802 scopus 로고    scopus 로고
    • Stable solutions for the bilaplacian with exponential nonlinearity
    • Dávila J., Dupaigne L., Guerra I., and Montenegro M. Stable solutions for the bilaplacian with exponential nonlinearity. SIAM J. Math. Anal. 39 2 (2007) 565-592
    • (2007) SIAM J. Math. Anal. , vol.39 , Issue.2 , pp. 565-592
    • Dávila, J.1    Dupaigne, L.2    Guerra, I.3    Montenegro, M.4
  • 16
    • 70349199396 scopus 로고    scopus 로고
    • Multiplicity of solutions for a fourth order equation with power-type nonlinearity
    • preprint
    • J. Dávila, I. Flores, I. Guerra, Multiplicity of solutions for a fourth order equation with power-type nonlinearity, preprint
    • Dávila, J.1    Flores, I.2    Guerra, I.3
  • 17
    • 70349207467 scopus 로고    scopus 로고
    • Geometry of phase space and solutions of semilinear elliptic equations in a ball
    • Dolbeault J., and Flores I. Geometry of phase space and solutions of semilinear elliptic equations in a ball. Trans. Amer. Math. Soc. 359 9 (2007) 4073-4087
    • (2007) Trans. Amer. Math. Soc. , vol.359 , Issue.9 , pp. 4073-4087
    • Dolbeault, J.1    Flores, I.2
  • 18
    • 33846329853 scopus 로고    scopus 로고
    • The Dirichlet problem for supercritical biharmonic equations with power-type nonlinearity
    • Ferrero A., and Grunau H.-C. The Dirichlet problem for supercritical biharmonic equations with power-type nonlinearity. J. Differential Equations 234 2 (2007) 582-606
    • (2007) J. Differential Equations , vol.234 , Issue.2 , pp. 582-606
    • Ferrero, A.1    Grunau, H.-C.2
  • 19
    • 52349124801 scopus 로고    scopus 로고
    • Supercritical biharmonic equations with power-type nonlinearity
    • Ferrero A., Grunau H.-C., and Karageorgis P. Supercritical biharmonic equations with power-type nonlinearity. Ann. Mat. Pura Appl. 188 (2009) 171-185
    • (2009) Ann. Mat. Pura Appl. , vol.188 , pp. 171-185
    • Ferrero, A.1    Grunau, H.-C.2    Karageorgis, P.3
  • 20
    • 61749088402 scopus 로고    scopus 로고
    • On solutions of second and fourth order elliptic equations with power-type nonlinearities
    • Ferrero A., and Warnault G. On solutions of second and fourth order elliptic equations with power-type nonlinearities. Nonlinear Anal. 70 8 (2009) 2889-2902
    • (2009) Nonlinear Anal. , vol.70 , Issue.8 , pp. 2889-2902
    • Ferrero, A.1    Warnault, G.2
  • 21
    • 1542511215 scopus 로고    scopus 로고
    • A resonance phenomenon for ground states of an elliptic equation of Emden-Fowler type
    • Flores I. A resonance phenomenon for ground states of an elliptic equation of Emden-Fowler type. J. Differential Equations 198 1 (2004) 1-15
    • (2004) J. Differential Equations , vol.198 , Issue.1 , pp. 1-15
    • Flores, I.1
  • 22
    • 70349194826 scopus 로고    scopus 로고
    • Singular solutions of the Brezis-Nirenberg problem in a ball
    • Flores I. Singular solutions of the Brezis-Nirenberg problem in a ball. Comm. Pure Appl. Anal. 8 2 (2009) 673-682
    • (2009) Comm. Pure Appl. Anal. , vol.8 , Issue.2 , pp. 673-682
    • Flores, I.1
  • 24
    • 33644899384 scopus 로고    scopus 로고
    • Radial entire solutions for supercritical biharmonic equations
    • Gazzola F., and Grunau H. Radial entire solutions for supercritical biharmonic equations. Math. Ann. 334 4 (2006) 905-936
    • (2006) Math. Ann. , vol.334 , Issue.4 , pp. 905-936
    • Gazzola, F.1    Grunau, H.2
  • 25
    • 0000247179 scopus 로고
    • Some problems in the theory of quasilinear equations
    • Section 15, due to G.I. Barenblatt
    • Gelfand I.M. Some problems in the theory of quasilinear equations. Section 15, due to G.I. Barenblatt. Amer. Math. Soc. Transl. Ser. 2 29 (1963) 295-381
    • (1963) Amer. Math. Soc. Transl. Ser. 2 , vol.29 , pp. 295-381
    • Gelfand, I.M.1
  • 26
    • 0041625080 scopus 로고    scopus 로고
    • Elliptic Partial Differential Equations of Second Order
    • Springer-Verlag, Berlin
    • Gilbarg D., and Trudinger N.S. Elliptic Partial Differential Equations of Second Order. Classics in Mathematics (2001), Springer-Verlag, Berlin
    • (2001) Classics in Mathematics
    • Gilbarg, D.1    Trudinger, N.S.2
  • 27
    • 0031524027 scopus 로고    scopus 로고
    • Positivity for equations involving polyharmonic operators with Dirichlet boundary conditions
    • Grunau H., and Sweers G. Positivity for equations involving polyharmonic operators with Dirichlet boundary conditions. Math. Ann. 307 4 (1997) 589-626
    • (1997) Math. Ann. , vol.307 , Issue.4 , pp. 589-626
    • Grunau, H.1    Sweers, G.2
  • 28
    • 0003235528 scopus 로고
    • Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields
    • Springer-Verlag, New York Revised and corrected reprint of the 1983 original
    • Guckenheimer J., and Holmes P. Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields. Applied Mathematical Sciences vol. 42 (1990), Springer-Verlag, New York Revised and corrected reprint of the 1983 original
    • (1990) Applied Mathematical Sciences , vol.42
    • Guckenheimer, J.1    Holmes, P.2
  • 29
    • 70349218381 scopus 로고    scopus 로고
    • On a fourth order nonlinear elliptic equation with negative exponent
    • Guo Z., and Wei J. On a fourth order nonlinear elliptic equation with negative exponent. SIAM J. Math. Anal. 40 5 (2009) 2034-2054
    • (2009) SIAM J. Math. Anal. , vol.40 , Issue.5 , pp. 2034-2054
    • Guo, Z.1    Wei, J.2
  • 31
    • 17944378468 scopus 로고    scopus 로고
    • Ordinary Differential Equations
    • Society for Industrial and Applied Mathematics (SIAM), Philadelphia, PA
    • Hartman P. Ordinary Differential Equations. Classics in Applied Mathematics vol. 38 (2002), Society for Industrial and Applied Mathematics (SIAM), Philadelphia, PA
    • (2002) Classics in Applied Mathematics , vol.38
    • Hartman, P.1
  • 32
    • 0015557517 scopus 로고
    • Quasilinear Dirichlet problems driven by positive sources
    • Joseph D.D., and Lundgren T.S. Quasilinear Dirichlet problems driven by positive sources. Arch. Ration. Mech. Anal. 49 (1972) 241-269
    • (1972) Arch. Ration. Mech. Anal. , vol.49 , pp. 241-269
    • Joseph, D.D.1    Lundgren, T.S.2
  • 33
    • 61749087270 scopus 로고    scopus 로고
    • Stability and intersection properties of solutions to the nonlinear biharmonic equation
    • preprint
    • P. Karageorgis, Stability and intersection properties of solutions to the nonlinear biharmonic equation, preprint
    • Karageorgis, P.1
  • 34
    • 0001751654 scopus 로고
    • On the existence of positive solutions of semilinear elliptic equations
    • Lions P.-L. On the existence of positive solutions of semilinear elliptic equations. SIAM Rev. 24 4 (1982) 441-467
    • (1982) SIAM Rev. , vol.24 , Issue.4 , pp. 441-467
    • Lions, P.-L.1
  • 36
    • 2442563160 scopus 로고    scopus 로고
    • Radial solutions of singular nonlinear biharmonic equations and applications to conformal geometry
    • No. 37, 13 pp
    • McKenna P.J., and Reichel W. Radial solutions of singular nonlinear biharmonic equations and applications to conformal geometry. Electron. J. Differential Equations (2003) No. 37, 13 pp
    • (2003) Electron. J. Differential Equations
    • McKenna, P.J.1    Reichel, W.2
  • 37
    • 0002047118 scopus 로고    scopus 로고
    • A priori estimates and the absence of solutions of nonlinear partial differential equations and inequalities
    • Mitidieri E., and Pokhozhaev S.I. A priori estimates and the absence of solutions of nonlinear partial differential equations and inequalities. Proc. Steklov Inst. Math. 234 3 (2001) 1-362
    • (2001) Proc. Steklov Inst. Math. , vol.234 , Issue.3 , pp. 1-362
    • Mitidieri, E.1    Pokhozhaev, S.I.2
  • 38
    • 49849128478 scopus 로고
    • On Morse-Smale dynamical systems
    • Palis J. On Morse-Smale dynamical systems. Topology 8 (1968) 385-404
    • (1968) Topology , vol.8 , pp. 385-404
    • Palis, J.1


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