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Annales Polonici Mathematici

2000 | 75 | 3 | 257-270
Tytuł artykułu

Multiple positive solutions to singular boundary value problems for superlinear second order FDEs

Autorzy
Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
We study the existence of positive solutions to the singular boundary value problem for a second-order FDE

⎧ u'' + q(t) f(t,u(w(t))) = 0, for almost all 0 < t < 1,
⎨ u(t) = ξ(t), a ≤ t ≤ 0,
⎩ u(t) = η(t), 1 ≤ t ≤ b,

where q(t) may be singular at t = 0 and t = 1, f(t,u) may be superlinear at u = ∞ and singular at u = 0.
Słowa kluczowe
EN
Czasopismo
Rocznik
Tom
Numer
Strony
257-270
Opis fizyczny
Daty
wydano
2000
otrzymano
2000-04-04
Twórcy
autor
• Department of Mathematics, Northeast Normal University, Changchun 130024, P.R. China
Bibliografia
• [1] R. P. Agarwal and D. O'Regan, Singular boundary value problems for superlinear second ordinary and delay differential equations, J. Differential Equations 130 (1996), 335-355.
• [2] R. P. Agarwal and D. O'Regan, Nonlinear superlinear singular and nonsingular second order boundary value problems, ibid. 143 (1998), 60-95.
• [3] J. V. Baxley, A singular nonlinear boundary value problem: Membrane response of a spherical cap, SIAM J. Appl. Math. 48 (1988), 497-505.
• [4] L. E. Bobisud, D. O'Regan and W. D. Royalty, Singular boundary value problems, Appl. Anal. 23 (1986), 233-243.
• [5] J. E. Bouillet and S. M. Gomes, An equation with a singular nonlinearity related to diffusion problems in one dimension, Quart. Appl. Math. 42 (1985), 395-402.
• [6] A. Callegari and A. Nachman, Some singular nonlinear differential equations arising in boundary layer theory, J. Math. Anal. Appl. 64 (1978), 96-105.
• [7] L. H. Erbe and Q. K. Kong, Boundary value problems for singular second-order functional differential equations, J. Comput. Appl. Math. 53 (1994), 377-388.
• [8] L. H. Erbe, Q. K. Kong and B. G. Zhang, Oscillation Theory and Boundary Value Problems in Functional Differential Equations, Dekker, New York, 1995.
• [9] L. H. Erbe, Z. C. Wang and L. T. Li, Boundary value problems for second order mixed type functional, differential equations, in: Boundary Value Problems for Functional Differential Equations, World Sci., 1995, 143-151.
• [10] J. A. Gatica, G. E. Hernandez and P. Waltman, Radially symmetric solutions of a class of singular elliptic equations, Proc. Edinburgh Math. Soc. 33 (1990), 168-180.
• [11] J. A. Gatica, V. Oliker and P. Waltman, Singular nonlinear boundary value problems for second order differential equations, J. Differential Equations 79 (1989), 62-78.
• [12] S. M. Gomes and J. Sprekels, Krasonselskii's Theorem on operators compressing a cone: Application to some singular boundary value problems, J. Math. Anal. Appl. 153 (1990), 443-459.
• [13] J. Janus and J. Myjak, A generalized Emden-Fowler equation with a negative exponent, Nonlinear Anal. 23 (1994), 953-970.
• [14] D. Q. Jiang and J. Y. Wang, On boundary value problems for singular second-order functional differential equations, J. Comput. Appl. Math. 116 (2000), 231-241.
• [15] D. Q. Jiang and P. X. Weng, Existence of positive solutions for boundary value problems of second-order functional differential equations, Electron. J. Qual. Theory Differ. Equ. 1998, no. 6, 13 pp.
• [16] M. A. Krasnosel'skiĭ, Positive Solutions of Operator Equations, Noordhoff, Groningen, 1964.
• [17] B. S. Lalli and B. G. Zhang, Boundary value problems for second order functional differential equations, Ann. Differential Equations 8 (1992), 261-268.
• [18] J. W. Lee and D. O'Regan, Existence results for differential delay equations - I, J. Differential Equations 102 (1993), 342-359.
• [19] J. W. Lee and D. O'Regan, Existence results for differential delay equations - II, Nonlinear Anal. 17 (1991), 683-702.
• [20] A. Nachman and A. Callegari, A nonlinear boundary value problems in the theory of pseudoplastic fluids, SIAM J. Appl. Math. 38 (1980), 275-281.
• [21] S. K. Ntouyas, Y. G. Sficas and P. C. Tsamatos, An existence principle for boundary value problems for second order functional-differential equations, Nonlinear Anal. 20 (1993), 215-222.
• [22] D. O'Regan, Positive solutions to singular and nonsingular second-order boundary value problems, J. Math. Anal. Appl. 142 (1989), 40-52.
• [23] D. O'Regan, Singular Dirchlet boundary value problems - I, superlinear and nonresonant case, Nonlinear Anal. 29 (1997), 221-245.
• [24] S. D. Taliaferro, A nonlinear singular boundary value problem, ibid. 3 (1979), 897-904.
• [25] C. J. Van Duijn, S. M. Gomes and H. F. Zhang, On a class of similarity solutions of the equation $u_t = (|u|^{m-1}u_x)_x$ with m > -1, IMA J. Appl. Math. 41 (1988), 147-163.
• [26] J. Y. Wang, A two-point boundary value problem with singularity, Northeast. Math. J. 3 (1987), 281-291.
• [27] J. Y. Wang, A free boundary problem for a generalized diffusion equation, Nonlinear Anal. 14 (1990), 691-700.
• [28] J. Y. Wang, On positive solutions of singular nonlinear two-point boundary problems, J. Differential Equations 107 (1994), 163-174.
• [29] J. Y. Wang, Solvability of singular nonlinear two-point boundary problems, Nonlinear Anal. 24 (1995), 555-561.
• [30] J. Y. Wang and W. J. Gao, A singular boundary value problem for the one-dimensional p-Laplacian, J. Math. Anal. Appl. 201 (1996), 851-866.
• [31] J. Y. Wang and J. Jiang, The existence of positive solutions to a singular nonlinear boundary value problem, ibid. 176 (1993), 322-329.
• [32] H. J. Weinischke, On finite displacement of circular elastic membranes, Math. Methods Appl. Sci. 9 (1987), 76-98.
• [33] P. X. Weng, Boundary value problems for second order mixed-type functional-differential equations, Appl. Math. J. Chinese Univ. Ser. B 12 (1997), 155-164.
• [34] P. X. Weng and D. Q. Jiang, Existence of positive solutions for boundary value problem of second-order FDE, Comput. Math. Appl. 37 (1999), 1-9.
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Bibliografia
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