메뉴 건너뛰기




Volumn 251, Issue , 2003, Pages 101-107

A monotone iterative scheme for a nonlinear second order equation based on a generalized anti-maximum principle

Author keywords

Anti maximum principle; Lower and upper solutions; Monotone iterative scheme

Indexed keywords


EID: 0037232881     PISSN: 0025584X     EISSN: None     Source Type: Journal    
DOI: 10.1002/mana.200310033     Document Type: Article
Times cited : (54)

References (16)
  • 1
    • 0000638780 scopus 로고
    • Elliptic equations with noninvertible Fredholm linear part and bounded nonlinearities
    • H. Amann, A. Ambrosetti, and G. Mancini, Elliptic equations with noninvertible Fredholm linear part and bounded nonlinearities, Math. Z. 158, 179-194 (1978).
    • (1978) Math. Z. , vol.158 , pp. 179-194
    • Amann, H.1    Ambrosetti, A.2    Mancini, G.3
  • 2
    • 0035840382 scopus 로고    scopus 로고
    • A constructive monotone iterative method for second-order BVP in the presence of lower and upper solutions
    • M. Cherpion, C. De Coster, and P. Habets, A constructive monotone iterative method for second-order BVP in the presence of lower and upper solutions, Appl. Math. Comp. 123, 75-91 (2001).
    • (2001) Appl. Math. Comp. , vol.123 , pp. 75-91
    • Cherpion, M.1    De Coster, C.2    Habets, P.3
  • 3
    • 0001873738 scopus 로고    scopus 로고
    • Upper and lower solutions in the theory of ODE boundary value problems: Classical and recent results
    • edited by F. Zanolin, CISM-ICMS (Springer-Verlag, New York)
    • C. De Coster and P. Habets, Upper and lower solutions in the theory of ODE boundary value problems: classical and recent results, in: Nonlinear Analysis and Boundary Value Problems for Ordinary Differential Equations, edited by F. Zanolin, CISM-ICMS 371 (Springer-Verlag, New York, 1996), pp. 1-78.
    • (1996) Nonlinear Analysis and Boundary Value Problems for Ordinary Differential Equations , vol.371 , pp. 1-78
    • De Coster, C.1    Habets, P.2
  • 4
    • 46149131254 scopus 로고
    • Periodic BVP for the forced Duffing equation
    • P. Drabek and S. Invernizzi, Periodic BVP for the forced Duffing equation, Nonlinear Anal. 10, 643-650 (1986).
    • (1986) Nonlinear Anal. , vol.10 , pp. 643-650
    • Drabek, P.1    Invernizzi, S.2
  • 5
    • 0034353694 scopus 로고    scopus 로고
    • Resonance pockets of Hill's equations with two-step potentials
    • S. B. Gan and M. R. Zhang, Resonance pockets of Hill's equations with two-step potentials, SIAM J. Math. Anal. 32, 651-664 (2000).
    • (2000) SIAM J. Math. Anal. , vol.32 , pp. 651-664
    • Gan, S.B.1    Zhang, M.R.2
  • 6
    • 0012535849 scopus 로고
    • Jumping nonlinearities for Neumann BVP's with positive forcing
    • Claremont, CA, Lecture Notes in Math. Springer-Verlag, Berlin
    • P. Habets, M. Ramos, and L. Sánchez, Jumping nonlinearities for Neumann BVP's with positive forcing, in: Delay Differential Equations and Dynamical Systems, (Claremont, CA, 1990), pp. 191-203, Lecture Notes in Math. 1475 (Springer-Verlag, Berlin, 1991).
    • (1990) Delay Differential Equations and Dynamical Systems , vol.1475 , pp. 191-203
    • Habets, P.1    Ramos, M.2    Sánchez, L.3
  • 7
    • 0025546181 scopus 로고
    • Large-amplitude periodic oscillations in suspension bridges: Some new connections with nonlinear analysis
    • A. C. Lazer and P. J. McKenna, Large-amplitude periodic oscillations in suspension bridges: some new connections with nonlinear analysis, SIAM Rev. 32, 537-578 (1990).
    • (1990) SIAM Rev. , vol.32 , pp. 537-578
    • Lazer, A.C.1    McKenna, P.J.2
  • 8
    • 0001839703 scopus 로고
    • On Poincaré perturbation theorem and a theorem of W. S. Loud
    • D. E. Leach, On Poincaré perturbation theorem and a theorem of W. S. Loud, J. Differential Equations 7, 34-53 (1970).
    • (1970) J. Differential Equations , vol.7 , pp. 34-53
    • Leach, D.E.1
  • 9
    • 0012585414 scopus 로고
    • Periodic solutions of nonlinear differential equations of Duffing type
    • Benjamin, New York
    • W. S. Loud, Periodic solutions of nonlinear differential equations of Duffing type, in: Proc. U.S.-Japan Seminar on Differential and Functional Equations (Benjamin, New York, 1967), pp. 199-224.
    • (1967) Proc. U.S.-Japan Seminar on Differential and Functional Equations , pp. 199-224
    • Loud, W.S.1
  • 10
    • 0036885507 scopus 로고    scopus 로고
    • The method of lower and upper solutions and the stability of periodic oscillations
    • D. Núñez, The method of lower and upper solutions and the stability of periodic oscillations, Nonlinear Anal. 51, 1207-1222 (2002).
    • (2002) Nonlinear Anal. , vol.51 , pp. 1207-1222
    • Núñez, D.1
  • 11
    • 0003001154 scopus 로고
    • Non-ordered lower and upper solutions and the solvability of the periodic problem for the Lienard and the Raileigh equations
    • P. Omari, Non-ordered lower and upper solutions and the solvability of the periodic problem for the Lienard and the Raileigh equations, Rend. Ist. Math. Univ. Trieste 20 (1988), 54-64.
    • (1988) Rend. Ist. Math. Univ. Trieste , vol.20 , pp. 54-64
    • Omari, P.1
  • 12
    • 0030188066 scopus 로고    scopus 로고
    • Periodic solutions of a newtonian equation: Stabylity by the third approximation
    • R. Ortega, Periodic solutions of a newtonian equation: stabylity by the third approximation, J. Diff. Equ. 128, 491-517 (1996).
    • (1996) J. Diff. Equ. , vol.128 , pp. 491-517
    • Ortega, R.1
  • 13
    • 38249011459 scopus 로고
    • Remarks on the lower and upper solution method for second and third-order periodic boundary value problems
    • P. Omari and M. Trombetta, Remarks on the lower and upper solution method for second and third-order periodic boundary value problems, Appl. Math. Comp. 50, 1-21 (1992).
    • (1992) Appl. Math. Comp. , vol.50 , pp. 1-21
    • Omari, P.1    Trombetta, M.2
  • 14
    • 34250392866 scopus 로고
    • Best constant in Sobolev inequality
    • G. Talenti, Best constant in Sobolev inequality, Ann. Mat. Pura Appl. 110(4), 353-372 (1976).
    • (1976) Ann. Mat. Pura Appl. , vol.110 , Issue.4 , pp. 353-372
    • Talenti, G.1
  • 15
    • 0034272121 scopus 로고    scopus 로고
    • Existence and uniqueness of elliptic periodic solutions of the Brillouin electron beam focusing system
    • P. Torres, Existence and uniqueness of elliptic periodic solutions of the Brillouin electron beam focusing system, Math. Meth. Appl. Sci. 23, 1139-1143 (2000).
    • (2000) Math. Meth. Appl. Sci. , vol.23 , pp. 1139-1143
    • Torres, P.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.