메뉴 건너뛰기




Volumn 145, Issue 2, 1998, Pages 420-452

Existence and Localization of Solution for Second Order Elliptic BVP in Presence of Lower and Upper Solutions without Any Order

Author keywords

Lower and upper solutions; elliptic equations; degree; existence and localization; multiplicity; p Laplacian

Indexed keywords


EID: 0000908135     PISSN: 00220396     EISSN: None     Source Type: Journal    
DOI: 10.1006/jdeq.1998.3423     Document Type: Article
Times cited : (59)

References (36)
  • 1
    • 0001753682 scopus 로고
    • On the number of solutions of nonlinear equations in ordered Banach spaces
    • Amann H. On the number of solutions of nonlinear equations in ordered Banach spaces. J. Funct. Anal. 11:1972;346-384.
    • (1972) J. Funct. Anal. , vol.11 , pp. 346-384
    • Amann, H.1
  • 2
    • 0017014016 scopus 로고
    • Fixed point equations and nonlinear eigenvalue problems in ordered Banach spaces
    • Amann H. Fixed point equations and nonlinear eigenvalue problems in ordered Banach spaces. SIAM Review. 18:1976;620-709.
    • (1976) SIAM Review , vol.18 , pp. 620-709
    • Amann, H.1
  • 3
    • 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
  • 4
    • 0000934232 scopus 로고
    • On some existence theorems for semilinear elliptic equations
    • Amann H., Crandall M. On some existence theorems for semilinear elliptic equations. Indiana Univ. Math. J. 27:1978;779-790.
    • (1978) Indiana Univ. Math. J. , vol.27 , pp. 779-790
    • Amann, H.1    Crandall, M.2
  • 5
    • 0011831509 scopus 로고
    • Theorems of existence and multiplicity for nonlinear elliptic problems with noninvertible linear part
    • Ambrosetti A., Mancini G. Theorems of existence and multiplicity for nonlinear elliptic problems with noninvertible linear part. Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4). 5:1978;15-28.
    • (1978) Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4) , vol.5 , pp. 15-28
    • Ambrosetti, A.1    Mancini, G.2
  • 7
    • 0000623205 scopus 로고
    • Simplicité et isolation de la première valeur propre dup
    • Anane A. Simplicité et isolation de la première valeur propre dup. C.R. Acad. Sci. Paris. 305:1987;725-728.
    • (1987) C.R. Acad. Sci. Paris , vol.305 , pp. 725-728
    • Anane, A.1
  • 8
    • 0040071187 scopus 로고
    • Monotone methods for periodic solutions of second order scalar functional differential equations
    • Bellen A. Monotone methods for periodic solutions of second order scalar functional differential equations. Numer. Math. 42:1983;15-30.
    • (1983) Numer. Math. , vol.42 , pp. 15-30
    • Bellen, A.1
  • 10
    • 0030589786 scopus 로고    scopus 로고
    • A positive operator approach to the Neumann problem for the second order ODE
    • Cabada A., Sanchez L. A positive operator approach to the Neumann problem for the second order ODE. J. Math. Anal. Appl. 204:1996;774-785.
    • (1996) J. Math. Anal. Appl. , vol.204 , pp. 774-785
    • Cabada, A.1    Sanchez, L.2
  • 11
    • 0040058718 scopus 로고    scopus 로고
    • On semilinear problem with nonlinearities depending only on the derivatives
    • Canada A., Drabek P. On semilinear problem with nonlinearities depending only on the derivatives. SIAM J. Math. Anal. 27:1996;543-557.
    • (1996) SIAM J. Math. Anal. , vol.27 , pp. 543-557
    • Canada, A.1    Drabek, P.2
  • 13
    • 0003283380 scopus 로고
    • Nonlinear Partial Differential Equations and Free Boundaries. Vol. 1: Elliptic Equations
    • London: Pitman
    • Diaz J. I. Nonlinear Partial Differential Equations and Free Boundaries. Vol. 1: Elliptic Equations. Pitman Research Notes in Math. 106:1985;Pitman, London.
    • (1985) Pitman Research Notes in Math. , vol.106
    • Diaz, J.I.1
  • 14
    • 84966222408 scopus 로고
    • On the existence of periodic solutions for scalar second order differential equations when only the asymptotic behavior of the potential is known
    • Fonda A. On the existence of periodic solutions for scalar second order differential equations when only the asymptotic behavior of the potential is known. Proc. Amer. Math. Soc. 119:1993;439-445.
    • (1993) Proc. Amer. Math. Soc. , vol.119 , pp. 439-445
    • Fonda, A.1
  • 15
    • 38249024579 scopus 로고
    • Periodic solutions of asymptotically positively homogeneous differential equations
    • Fonda A., Habets P. Periodic solutions of asymptotically positively homogeneous differential equations. J. Differential Equations. 81:1989;68-97.
    • (1989) J. Differential Equations , vol.81 , pp. 68-97
    • Fonda, A.1    Habets, P.2
  • 16
    • 0001918237 scopus 로고
    • Periodic solutions of a second order ordinary differential equation: A necessary and sufficient condition for nonresonance
    • Gossez J. P., Omari P. Periodic solutions of a second order ordinary differential equation: A necessary and sufficient condition for nonresonance. J. Differential Equations. 94:1991;67-82.
    • (1991) J. Differential Equations , vol.94 , pp. 67-82
    • Gossez, J.P.1    Omari, P.2
  • 17
    • 84968503405 scopus 로고
    • A necessary and sufficient condition of nonresonance for a semilinear Neumann problem
    • Gossez J. P., Omari P. A necessary and sufficient condition of nonresonance for a semilinear Neumann problem. Proc. Amer. Math. Soc. 114:1992;433-442.
    • (1992) Proc. Amer. Math. Soc. , vol.114 , pp. 433-442
    • Gossez, J.P.1    Omari, P.2
  • 18
    • 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
  • 19
    • 0001728005 scopus 로고
    • On a semilinear elliptic Neumann problem with asymmetric nonlinearities
    • Gossez J. P., Omari P. On a semilinear elliptic Neumann problem with asymmetric nonlinearities. Trans. Amer. Math. Soc. 347:1995;2553-2562.
    • (1995) Trans. Amer. Math. Soc. , vol.347 , pp. 2553-2562
    • Gossez, J.P.1    Omari, P.2
  • 20
    • 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. Top. Meth. Nonlinear Anal. 8:1996;25-56.
    • (1996) Top. Meth. Nonlinear Anal. , vol.8 , pp. 25-56
    • Habets, P.1    Omari, P.2
  • 21
    • 21344472294 scopus 로고
    • Nonresonance conditions on the potential with respect to the Fucik spectrum for the periodic boundary value problem
    • Habets P., Omari P., Zanolin F. Nonresonance conditions on the potential with respect to the Fucik spectrum for the periodic boundary value problem. Rocky Mountain J. Math. 25:1995;1305-1340.
    • (1995) Rocky Mountain J. Math. , vol.25 , pp. 1305-1340
    • Habets, P.1    Omari, P.2    Zanolin, F.3
  • 22
    • 0031485353 scopus 로고    scopus 로고
    • A two-point problem with nonlinearity depending only of the derivative
    • Habets P., Sanchez L. A two-point problem with nonlinearity depending only of the derivative. SIAM J. Math. Anal. 28:1997;1205-1211.
    • (1997) SIAM J. Math. Anal. , vol.28 , pp. 1205-1211
    • Habets, P.1    Sanchez, L.2
  • 23
    • 84980157300 scopus 로고
    • Invariant criteria for existence of solutions to second-order quasilinear elliptic equations
    • Kazdan J. K., Kramer R. J. Invariant criteria for existence of solutions to second-order quasilinear elliptic equations. Comm. Pure Appl. Math. 31:1978;619-645.
    • (1978) Comm. Pure Appl. Math. , vol.31 , pp. 619-645
    • Kazdan, J.K.1    Kramer, R.J.2
  • 24
    • 0000405695 scopus 로고
    • Boundary regularity for solutions of degenerate elliptic equations
    • Lieberman G. M. Boundary regularity for solutions of degenerate elliptic equations. Nonlinear Anal. 12:1988;1203-1219.
    • (1988) Nonlinear Anal. , vol.12 , pp. 1203-1219
    • Lieberman, G.M.1
  • 25
    • 84971182202 scopus 로고
    • Upper and lower solutions and semilinear second order elliptic equations with nonlinear boundary conditions
    • Mawhin J., Schmitt K. Upper and lower solutions and semilinear second order elliptic equations with nonlinear boundary conditions. Proc. Roy. Soc. Edinburgh Sect. A. 97:1984;199-207.
    • (1984) Proc. Roy. Soc. Edinburgh Sect. a , vol.97 , pp. 199-207
    • Mawhin, J.1    Schmitt, K.2
  • 26
    • 84972577596 scopus 로고
    • On principally linear elliptic differential equations of the second order
    • Nagumo M. On principally linear elliptic differential equations of the second order. Osaka Math. J. 6:1954;207-229.
    • (1954) Osaka Math. J. , vol.6 , pp. 207-229
    • Nagumo, M.1
  • 28
    • 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
  • 29
    • 38249011459 scopus 로고
    • Remarks on the lower and upper solutions method for second and third order periodic BVP
    • Omari P., Trombetta M. Remarks on the lower and upper solutions method for second and third order periodic BVP. Appl. Math. Comput. 50:1992;1-21.
    • (1992) Appl. Math. Comput. , vol.50 , pp. 1-21
    • Omari, P.1    Trombetta, M.2
  • 30
    • 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
  • 31
    • 0001636688 scopus 로고
    • Boundary value problems for quasilinear second order elliptic equations
    • Schmitt K. Boundary value problems for quasilinear second order elliptic equations. Nonlinear Anal. 2:1978;263-309.
    • (1978) Nonlinear Anal. , vol.2 , pp. 263-309
    • Schmitt, K.1
  • 32
    • 0038886730 scopus 로고
    • Differential inequalities for second- And third-order equations
    • Schrader K. W. Differential inequalities for second- and third-order equations. J. Differential Equations. 23:1977;203-215.
    • (1977) J. Differential Equations , vol.23 , pp. 203-215
    • Schrader, K.W.1
  • 33
    • 0010173393 scopus 로고
    • Il problema dei valori ai limiti studiato in grande per le equazioni differenziali del secondo ordine
    • Scorza Dragoni G. Il problema dei valori ai limiti studiato in grande per le equazioni differenziali del secondo ordine. Giornale di Mat. (Battaglini). 69:1931;77-112.
    • (1931) Giornale di Mat. (Battaglini) , vol.69 , pp. 77-112
    • Scorza Dragoni, G.1
  • 34
    • 0011546288 scopus 로고
    • Some new fixed point theorems of increasing operators and applications
    • Jingxian Sun. Some new fixed point theorems of increasing operators and applications. Appl. Anal. 42:1991;263-273.
    • (1991) Appl. Anal. , vol.42 , pp. 263-273
    • Jingxian Sun1
  • 36
    • 0001335714 scopus 로고
    • A strong maximum principle for some quasilinear elliptic equations
    • Vazquez J. L. A strong maximum principle for some quasilinear elliptic equations. Appl. Math. Optim. 12:1984;191-202.
    • (1984) Appl. Math. Optim. , vol.12 , pp. 191-202
    • Vazquez, J.L.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.