메뉴 건너뛰기




Volumn 234, Issue 2, 2007, Pages 582-606

The Dirichlet problem for supercritical biharmonic equations with power-type nonlinearity

Author keywords

[No Author keywords available]

Indexed keywords


EID: 33846329853     PISSN: 00220396     EISSN: 10902732     Source Type: Journal    
DOI: 10.1016/j.jde.2006.11.007     Document Type: Article
Times cited : (31)

References (24)
  • 1
    • 84980075953 scopus 로고
    • Estimates near the boundary for solutions of elliptic partial differential equations satisfying general boundary conditions. I
    • Agmon S., Douglis A., and Nirenberg L. Estimates near the boundary for solutions of elliptic partial differential equations satisfying general boundary conditions. I. Comm. Pure Appl. Math. 12 (1959) 623-727
    • (1959) Comm. Pure Appl. Math. , vol.12 , pp. 623-727
    • Agmon, S.1    Douglis, A.2    Nirenberg, L.3
  • 2
    • 17444378460 scopus 로고    scopus 로고
    • A semilinear fourth order elliptic problem with exponential nonlinearity
    • Arioli G., Gazzola F., Grunau H.-Ch., and Mitidieri E. A semilinear fourth order elliptic problem with exponential nonlinearity. SIAM J. Math. Anal. 36 (2005) 1226-1258
    • (2005) SIAM J. Math. Anal. , vol.36 , pp. 1226-1258
    • Arioli, G.1    Gazzola, F.2    Grunau, H.-Ch.3    Mitidieri, E.4
  • 3
    • 17444403583 scopus 로고    scopus 로고
    • Some remarks on biharmonic elliptic problems with positive, increasing and convex nonlinearities
    • Berchio E., and Gazzola F. Some remarks on biharmonic elliptic problems with positive, increasing and convex nonlinearities. Electron. J. Differential Equations 2005 34 (2005) 1-20
    • (2005) Electron. J. Differential Equations , vol.2005 , Issue.34 , pp. 1-20
    • Berchio, E.1    Gazzola, F.2
  • 4
    • 0013197968 scopus 로고
    • Sulle funzioni di Green d'ordine m
    • Boggio T. Sulle funzioni di Green d'ordine m. Rend. Circ. Mat. Palermo 20 (1905) 97-135
    • (1905) Rend. Circ. Mat. Palermo , vol.20 , pp. 97-135
    • Boggio, T.1
  • 6
    • 0001471516 scopus 로고    scopus 로고
    • Blow up solutions of some nonlinear elliptic problems
    • Brezis H., and Vazquez J.L. Blow up solutions of some nonlinear elliptic problems. Rev. Mat. Univ. Complut. Madrid 10 (1997) 443-469
    • (1997) Rev. Mat. Univ. Complut. Madrid , vol.10 , pp. 443-469
    • Brezis, H.1    Vazquez, J.L.2
  • 7
    • 0001391309 scopus 로고
    • Uniqueness theorems for some fourth-order elliptic equations
    • Dalmasso R. Uniqueness theorems for some fourth-order elliptic equations. Proc. Amer. Math. Soc. 123 (1995) 1177-1183
    • (1995) Proc. Amer. Math. Soc. , vol.123 , pp. 1177-1183
    • Dalmasso, R.1
  • 8
    • 33846266538 scopus 로고    scopus 로고
    • J.I. Diaz, M. Lazzo, P.G. Schmidt, Large solutions of a polyharmonic equation with superlinear growth, preprint
  • 9
    • 33644899384 scopus 로고    scopus 로고
    • Radial entire solutions for supercritical biharmonic equations
    • Gazzola F., and Grunau H.-Ch. Radial entire solutions for supercritical biharmonic equations. Math. Ann. 334 (2006) 905-936
    • (2006) Math. Ann. , vol.334 , pp. 905-936
    • Gazzola, F.1    Grunau, H.-Ch.2
  • 10
    • 84980182383 scopus 로고
    • Global and local behavior of positive solutions of nonlinear elliptic equations
    • Gidas B., and Spruck J. Global and local behavior of positive solutions of nonlinear elliptic equations. Comm. Pure Appl. Math. 34 (1981) 525-598
    • (1981) Comm. Pure Appl. Math. , vol.34 , pp. 525-598
    • Gidas, B.1    Spruck, J.2
  • 11
    • 0040398598 scopus 로고    scopus 로고
    • Positivity properties of elliptic boundary value problems of higher order
    • Proc. 2nd World Congress of Nonlinear Analysts
    • Grunau H.-Ch., and Sweers G. Positivity properties of elliptic boundary value problems of higher order. Proc. 2nd World Congress of Nonlinear Analysts. Nonlinear Anal. 30 (1997) 5251-5258
    • (1997) Nonlinear Anal. , vol.30 , pp. 5251-5258
    • Grunau, H.-Ch.1    Sweers, G.2
  • 13
    • 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 (1973) 241-269
    • (1973) Arch. Ration. Mech. Anal. , vol.49 , pp. 241-269
    • Joseph, D.D.1    Lundgren, T.S.2
  • 14
    • 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 (1982) 441-467
    • (1982) SIAM Rev. , vol.24 , pp. 441-467
    • Lions, P.L.1
  • 15
    • 84972948243 scopus 로고
    • Sur une classe de problèmes nonlinéaires avec nonlinéarité positive, croissante, convexe
    • Mignot F., and Puel J.P. Sur une classe de problèmes nonlinéaires avec nonlinéarité positive, croissante, convexe. Comm. Partial Differential Equations 5 (1980) 791-836
    • (1980) Comm. Partial Differential Equations , vol.5 , pp. 791-836
    • Mignot, F.1    Puel, J.P.2
  • 16
    • 0002047118 scopus 로고    scopus 로고
    • Apriori estimates and blow-up of solutions to nonlinear partial differential equations and inequalities
    • (translated from Russian)
    • Mitidieri E., and Pohožaev S. Apriori estimates and blow-up of solutions to nonlinear partial differential equations and inequalities. Proc. Steklov Inst. Math. 234 (2001) 1-362 (translated from Russian)
    • (2001) Proc. Steklov Inst. Math. , vol.234 , pp. 1-362
    • Mitidieri, E.1    Pohožaev, S.2
  • 17
    • 0142211080 scopus 로고
    • On a priori estimates for positive solutions of a semilinear biharmonic equation in a ball
    • Oswald P. On a priori estimates for positive solutions of a semilinear biharmonic equation in a ball. Comment. Math. Univ. Carolin. 26 (1985) 565-577
    • (1985) Comment. Math. Univ. Carolin. , vol.26 , pp. 565-577
    • Oswald, P.1
  • 18
    • 0000514956 scopus 로고
    • Eigenfunctions of the equation Δ u + λ f (u) = 0
    • Pohožaev S.I. Eigenfunctions of the equation Δ u + λ f (u) = 0. Soviet Math. Dokl. 6 (1965) 1408-1411
    • (1965) Soviet Math. Dokl. , vol.6 , pp. 1408-1411
    • Pohožaev, S.I.1
  • 19
    • 33644882092 scopus 로고
    • n with a supercritical index of nonlinearity
    • English translation in
    • n with a supercritical index of nonlinearity. Dokl. Akad. Nauk SSSR 313 (1990) 1356-1360 English translation in
    • (1990) Dokl. Akad. Nauk SSSR , vol.313 , pp. 1356-1360
    • Pohožaev, S.I.1
  • 20
    • 0000939361 scopus 로고
    • n with a supercritical index of nonlinearity
    • n with a supercritical index of nonlinearity. Soviet Math. Dokl. 42 (1991) 215-219
    • (1991) Soviet Math. Dokl. , vol.42 , pp. 215-219
    • Pohožaev, S.I.1
  • 21
    • 0242593178 scopus 로고    scopus 로고
    • Uniqueness results for semilinear polyharmonic boundary value problems on conformally contractible domains, I
    • Reichel W. Uniqueness results for semilinear polyharmonic boundary value problems on conformally contractible domains, I. J. Math. Anal. Appl. 287 (2003) 61-74
    • (2003) J. Math. Anal. Appl. , vol.287 , pp. 61-74
    • Reichel, W.1
  • 22
    • 0242676986 scopus 로고    scopus 로고
    • Uniqueness results for semilinear polyharmonic boundary value problems on conformally contractible domains, II
    • Reichel W. Uniqueness results for semilinear polyharmonic boundary value problems on conformally contractible domains, II. J. Math. Anal. Appl. 287 (2003) 75-89
    • (2003) J. Math. Anal. Appl. , vol.287 , pp. 75-89
    • Reichel, W.1
  • 23
    • 0012284366 scopus 로고
    • A priori estimates and existence of positive solutions of a superlinear polyharmonic equation
    • Soranzo R. A priori estimates and existence of positive solutions of a superlinear polyharmonic equation. Dyn. Systems Appl. 3 (1994) 465-487
    • (1994) Dyn. Systems Appl. , vol.3 , pp. 465-487
    • Soranzo, R.1
  • 24
    • 84968512169 scopus 로고
    • On the Cauchy problem for reaction-diffusion equations
    • Wang X. On the Cauchy problem for reaction-diffusion equations. Trans. Amer. Math. Soc. 337 (1993) 549-590
    • (1993) Trans. Amer. Math. Soc. , vol.337 , pp. 549-590
    • Wang, X.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.