메뉴 건너뛰기




Volumn 175, Issue 1, 2000, Pages 52-88

Unstable Periodic Solutions of a Parabolic Problem in the Presence of Non-well-ordered Lower and Upper Solutions

Author keywords

[No Author keywords available]

Indexed keywords


EID: 0012942546     PISSN: 00221236     EISSN: None     Source Type: Journal    
DOI: 10.1006/jfan.2000.3600     Document Type: Article
Times cited : (28)

References (31)
  • 1
    • 0002312007 scopus 로고
    • Periodic solutions of semilinear parabolic equations
    • L. Cesari, R. Kannan, & H. F. Weinberger. New York: Academic Press
    • Amann H. Periodic solutions of semilinear parabolic equations. Cesari L., Kannan R., Weinberger H. F. Nonlinear Analysis. A Collection of Papers in Honor of E. Rothe. 1978;1-29 Academic Press, New York.
    • (1978) Nonlinear Analysis. A Collection of Papers in Honor of E. Rothe , pp. 1-29
    • Amann, H.1
  • 2
    • 0000638780 scopus 로고
    • Elliptic equations with noninvertible Fredholm linear part and bounded nonlinearities
    • Amann H., Ambrosetti A., Mancini G. Elliptic equations with noninvertible Fredholm linear part and bounded nonlinearities. Math. Z. 158:1978;179-194.
    • (1978) Math. Z. , vol.158 , pp. 179-194
    • Amann, H.1    Ambrosetti, A.2    Mancini, G.3
  • 3
    • 0002360528 scopus 로고
    • Periodic solutions of a quasilinear parabolic differential equation
    • Bange D. W. Periodic solutions of a quasilinear parabolic differential equation. J. Differential Equations. 17:1975;61-72.
    • (1975) J. Differential Equations , vol.17 , pp. 61-72
    • Bange, D.W.1
  • 4
    • 0041717827 scopus 로고
    • Invariant sets and the Hukuhara-Kneser property for systems of parabolic partial differential equations
    • Bebernes J. W., Schmitt K. Invariant sets and the Hukuhara-Kneser property for systems of parabolic partial differential equations. Rocky Mountain J. Math. 7:1977;557-567.
    • (1977) Rocky Mountain J. Math. , vol.7 , pp. 557-567
    • Bebernes, J.W.1    Schmitt, K.2
  • 5
    • 84968470255 scopus 로고
    • On the existence and boundedness of solutions of nonlinear partial differential equation of parabolic type
    • Bellman R. On the existence and boundedness of solutions of nonlinear partial differential equation of parabolic type. Trans. Amer. Math. Soc. 64:1948;21-44.
    • (1948) Trans. Amer. Math. Soc. , vol.64 , pp. 21-44
    • Bellman, R.1
  • 7
    • 0011453742 scopus 로고
    • On stable solutions of quasilinear periodic-parabolic problems
    • Dancer E. N., Hess P. On stable solutions of quasilinear periodic-parabolic problems. Ann. Scuola Norm. Sup. Pisa CL. Sci. (4). 14:1987;123-141.
    • (1987) Ann. Scuola Norm. Sup. Pisa CL. Sci. (4) , vol.14 , pp. 123-141
    • Dancer, E.N.1    Hess, P.2
  • 8
    • 0001283333 scopus 로고
    • Stability of fixed points for order-preserving discrete time dynamical systems
    • Dancer E. N., Hess P. Stability of fixed points for order-preserving discrete time dynamical systems. J. Reine Angew. Math. 419:1991;125-139.
    • (1991) J. Reine Angew. Math. , vol.419 , pp. 125-139
    • Dancer, E.N.1    Hess, P.2
  • 9
    • 0003227862 scopus 로고
    • Abstract Evolution Equations, Periodic Problems and Applications
    • Harlow: Longman Sci. Tech.
    • Dancers D., Koch Medina P. Abstract Evolution Equations, Periodic Problems and Applications. Pitman Res. Notes Mathematics. 279:1992;Longman Sci. Tech. Harlow.
    • (1992) Pitman Res. Notes Mathematics , vol.279
    • Dancers, D.1    Koch Medina, P.2
  • 10
    • 0032041648 scopus 로고    scopus 로고
    • Existence, localization, and instability of solutions in presence of non-well-ordered lower and upper solutions
    • De Coster C. Existence, localization, and instability of solutions in presence of non-well-ordered lower and upper solutions. C. R. Acad. Sci. Paris. 326:1998;935-940.
    • (1998) C. R. Acad. Sci. Paris , vol.326 , pp. 935-940
    • De Coster, C.1
  • 11
    • 0000908135 scopus 로고    scopus 로고
    • Existence and localization of solutions for elliptic problem in presence of lower and upper solutions without any order
    • De Coster C., Henrard M. Existence and localization of solutions for elliptic problem in presence of lower and upper solutions without any order. J. Differential Equations. 145:1998;420-452.
    • (1998) J. Differential Equations , vol.145 , pp. 420-452
    • De Coster, C.1    Henrard, M.2
  • 13
    • 51249179923 scopus 로고
    • Nonlinear parabolic boundary value problems with upper and lower solutions
    • Deuel J., Hess P. Nonlinear parabolic boundary value problems with upper and lower solutions. Israel J. Math. 29:1978;92-104.
    • (1978) Israel J. Math. , vol.29 , pp. 92-104
    • Deuel, J.1    Hess, P.2
  • 14
    • 0011628445 scopus 로고
    • Non-ordered lower and upper solutions in semilinear elliptic problems
    • Gossez J. P., Omari P. Non-ordered lower and upper solutions in semilinear elliptic problems. Comm. Partial Differential Equations. 19:1994;1163-1184.
    • (1994) Comm. Partial Differential Equations , vol.19 , pp. 1163-1184
    • Gossez, J.P.1    Omari, P.2
  • 15
    • 0002816349 scopus 로고    scopus 로고
    • Existence and localization of solutions of second order elliptic problems using lower and upper solutions in the reversed order
    • Habets P., Omari P. Existence and localization of solutions of second order elliptic problems using lower and upper solutions in the reversed order. Topol. Meth. Nonlinear Anal. 8:1996;25-56.
    • (1996) Topol. Meth. Nonlinear Anal. , vol.8 , pp. 25-56
    • Habets, P.1    Omari, P.2
  • 16
    • 0003323485 scopus 로고
    • Periodic-Parabolic Boundary Value Problems and Positivity
    • Harlow: Longman Sci. Tech.
    • Hess P. Periodic-Parabolic Boundary Value Problems and Positivity. Pitman Res. Notes Mathematics. 247:1991;Longman Sci. Tech. Harlow.
    • (1991) Pitman Res. Notes Mathematics , vol.247
    • Hess, P.1
  • 17
    • 0042376684 scopus 로고    scopus 로고
    • Existence of stable and unstable solutions for semilinear parabolic problems with a jumping nonlinearity
    • Hirano N., Kim W. S. Existence of stable and unstable solutions for semilinear parabolic problems with a jumping nonlinearity. Nonlinear Anal. 26:1996;1143-1160.
    • (1996) Nonlinear Anal. , vol.26 , pp. 1143-1160
    • Hirano, N.1    Kim, W.S.2
  • 18
    • 0038328502 scopus 로고    scopus 로고
    • Multiplicity and stability result for semilinear parabolic equations
    • Hirano N., Kim W. S. Multiplicity and stability result for semilinear parabolic equations. Discrete Continuous Dynam. Systems. 2:1996;271-280.
    • (1996) Discrete Continuous Dynam. Systems , vol.2 , pp. 271-280
    • Hirano, N.1    Kim, W.S.2
  • 19
    • 33745815315 scopus 로고
    • Stability and convergence in strongly monotone dynamical systems
    • Hirsch M. W. Stability and convergence in strongly monotone dynamical systems. J. Reine Angew. Math. 383:1988;1-53.
    • (1988) J. Reine Angew. Math. , vol.383 , pp. 1-53
    • Hirsch, M.W.1
  • 20
    • 0347855913 scopus 로고
    • A test for the existence of periodic solutions to parabolic equations
    • Kolesov Ju. S. A test for the existence of periodic solutions to parabolic equations. Dokl. Akad. Nauk. SSSR. 170:1966;1013-1015.
    • (1966) Dokl. Akad. Nauk. SSSR , vol.170 , pp. 1013-1015
    • Kolesov, Ju.s.1
  • 21
    • 0347225733 scopus 로고
    • Schauder's principle and the stability of periodic solutions
    • Kolesov Ju. S. Schauder's principle and the stability of periodic solutions. Dokl. Akad. Nauk SSSR. 188:1969.
    • (1969) Dokl. Akad. Nauk SSSR , vol.188
    • Kolesov, Ju.s.1
  • 22
    • 0347855912 scopus 로고
    • Periodic solutions of parabolic partial differential equations
    • Kusano T. Periodic solutions of parabolic partial differential equations. Sūgaku. 18:1966;104-106.
    • (1966) Sūgaku , vol.18 , pp. 104-106
    • Kusano, T.1
  • 23
    • 0347225731 scopus 로고
    • Some remarks on periodic solutions of parabolic differential equations
    • A. R. Bednarek, & L. Cesari. New York: Academic Press
    • Lazer A. C. Some remarks on periodic solutions of parabolic differential equations. Bednarek A. R., Cesari L. Dynamical Systems II. 1982;227-246 Academic Press, New York.
    • (1982) Dynamical Systems II , pp. 227-246
    • Lazer, A.C.1
  • 24
    • 85009592686 scopus 로고
    • Asymptotic behavior and stability of solutions of semilinear diffusion equations
    • Matano H. Asymptotic behavior and stability of solutions of semilinear diffusion equations. Publ. Res. Inst. Math. Sci. 15:1979;401-454.
    • (1979) Publ. Res. Inst. Math. Sci. , vol.15 , pp. 401-454
    • Matano, H.1
  • 25
    • 0001166664 scopus 로고
    • Existence of nontrivial unstable sets for equilibriums of strongly order-preserving systems
    • Matano H. Existence of nontrivial unstable sets for equilibriums of strongly order-preserving systems. J. Fac. Sci. Univ. Tokyo Sect. IA Math. 30:1983;645-673.
    • (1983) J. Fac. Sci. Univ. Tokyo Sect. IA Math. , vol.30 , pp. 645-673
    • Matano, H.1
  • 26
    • 0342709521 scopus 로고
    • Parabolic differential inequalities and Chaplighin's method
    • Mlak M. Parabolic differential inequalities and Chaplighin's method. Ann. Polon. Math. 8:1960;139-152.
    • (1960) Ann. Polon. Math. , vol.8 , pp. 139-152
    • Mlak, M.1
  • 27
    • 0003001154 scopus 로고
    • Non-ordered lower and upper solutions and solvability of the periodic problem for the Liénard and the Rayleigh equations
    • Omari P. Non-ordered lower and upper solutions and solvability of the periodic problem for the Liénard and the Rayleigh equations. Rend. Istit. Mat. Univ. Trieste. 20:1988;54-64.
    • (1988) Rend. Istit. Mat. Univ. Trieste , vol.20 , pp. 54-64
    • Omari, P.1
  • 31
    • 0001314482 scopus 로고
    • Monotone methods in nonlinear elliptic and parabolic boundary value problems
    • Sattinger D. H. Monotone methods in nonlinear elliptic and parabolic boundary value problems. Indiana Univ. Math. J. 21:1972;979-1000.
    • (1972) Indiana Univ. Math. J. , vol.21 , pp. 979-1000
    • Sattinger, D.H.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.