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Tytuł artykułu

A singular nonlinear boundary value problem with Neumann conditions

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Treść / Zawartość
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Języki publikacji
EN
Abstrakty
EN
We study the existence of solutions for the equations x" plmin g(t, x) = h(t), t mem (0, 1) with Neumann boundary conditions, where g: [0, 1] x (0, +infin) arr [0, +infin] and h: [0, 1] arr R are continuous and g(t, ·) is singular at 0 for each t mem [0, 1].
Rocznik
Strony
227--241
Opis fizyczny
Bibliogr. 21 poz.
Twórcy
autor
  • AGH University of Science and Technology, Faculty of Applied Mathematics, al. Mickiewicza 30, 30-059 Cracow, Poland, janus@uci.agh.edu.pl
Bibliografia
  • [1] Bobisud L.E., O'Regan D.: Existence of solutions to some singular initial value problems. J. Math. Anal. Appl., 133 (1988), 214-230.
  • [2] Bobisud L.E., O'Regan D., Royalty W. D.: Solvability of some nonlinear boun­dary value problems. Nonlinear Anal. 12 (1988), 855-869.
  • [3] Callegari A. J., Friedman A.: An analytical solution of a nonlinear singular boundary value problem in the theory of viscous fluids. J. Math. Anal. Appl. 21 (1968), 510-529.
  • [4] Callegari A. J., Nachman A.: Some singular nonlinear differential equations ari­sing in boundary layer theory. J. Math. Anal. Appl. 64 (1978), 96-105.
  • [5] Fonda A., Manasevich R., Zanolin F.: Subharmonic solutions for some 2nd-order differential-equations with singularities. SIAM. J. Math. Anal. 24 (1993), 1294-1311.
  • [6] Gacki H., Janus J.: On periodic solutions of second order nonlinear differential equations with singularities. Comment. Math. Prace Mat. 30 (1991), 292-299.
  • [7] Gaines R.E., Mawhin J.L.; Coincidence degree and nonlinear differential equ­ations. Lecture Notes in Math., vol. 568, Berlin, Springer-Verlag, 1977.
  • [8] Gatica J. A., Oliker V., Waltman P.: Singular nonlinear boundary value problems for second-order ordinary differential equations. J. Differential Equations 79
  • (1989), 62-78.
  • [9] Habets P., Zanolin F.: Upper and lower solutions for a generalized Emden-Fowler equatio. J. Math. Anal. Appl. 181 (1994), 684-700.
  • [10] Habets P.; Zanolin F.: Positive solutions for a class of singular boundary value problems. Boll. Un. Mat. Ital. A(7) 9 (1995) 2, 273-286.
  • [11] Janus J., Myjak J.: A generalized Emden-Fowler equation with a negative expo­nent. Nonlinear Anal. TMA 23 (1994), 952-970.
  • [12] Lazer A. C., Solimini S.: On periodic solutions of nonlinear differential equations with singularities. Proc. Amer. Math. Soc. 99 (1987), 109-114.
  • [13] Luning C.D., Perry W. L.: Positive solutions of negative exponent generalized Emden-Fowler boundary value problems. SIAM J. Math. Anal. 12 (1981), 874-879.
  • [14] Nachman A., Callegari A. J.: A nonlinear boundary value problem in the theory of pseudoplastic fluids. SIAM J. Appl. Math. (1980), 275-281.
  • [15] Nachman A., Taliaferro S.: Mass transfer into boundary layers for power law fluids. Proc. R. Soc. Lond. A 365 (1979), 313-326.
  • [16] O'Regan D.: Positive Solutions to singular and non-singular second-order boun­dary value problem. J. Math. Anal. Appl. 142, 1, 1989.
  • [17] Schmitt K.: Boundary value problems for quasilinear second order elliptic equ­ations. Nonlinear Anal. 2 (1978), 263-309.
  • [18] Taliaferro S.: On the positive solutions of y" + {t)y~x = 0. Nonlinear Anal. 2 (1978), 437-446.
  • [19] Taliaferro S.: A nonlinear singular boundary value problem. Nonlinear Anal. 3 (1979), 897-904.
  • [20] Tineo A.: Existence theorem for a singular two-point Dirichlet problem. Nonlinear Anal. TMA 19 (1992), 323-333.
  • [21] Wong J.S.W.: On the generalized Emden-Fowler equation. SIAM Rev., 17 (1975), 339-360.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-article-AGH4-0003-0046
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