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2009 | 7 | 4 | 694-716

Tytuł artykułu

Positive and maximal positive solutions of singular mixed boundary value problem

Treść / Zawartość

Warianty tytułu

Języki publikacji

EN

Abstrakty

EN
The paper is concerned with existence results for positive solutions and maximal positive solutions of singular mixed boundary value problems. Nonlinearities h(t;x;y) in differential equations admit a time singularity at t=0 and/or at t=T and a strong singularity at x=0.

Wydawca

Czasopismo

Rocznik

Tom

7

Numer

4

Strony

694-716

Opis fizyczny

Daty

wydano
2009-12-01
online
2009-10-31

Twórcy

autor
  • Department of Mathematics, National University of Ireland, Galway, Ireland
  • Department of Mathematical Analysis, Faculty of Science, Palacký University, Olomouc, Czech Republic

Bibliografia

  • [1] Agarwal R.P., O’Regan D., Singular differential and integral equations with applications, Kluwer, Dordrecht, 2003
  • [2] Agarwal R.P., O’Regan D., Singular problems motivated from classical upper and lower solutions, Acta Math. Hungar., 2003, 100, 245–256 http://dx.doi.org/10.1023/A:1025045626822[Crossref]
  • [3] Agarwal R.P., O’Regan D., Staněek S., Existence of positive solutions for boundary-value problems with singularities in phase variables, Proc. Edinburgh Math. Soc., 2004, 47, 1–13 http://dx.doi.org/10.1017/S0013091503000105[Crossref]
  • [4] Agarwal R.P., Staněek S., Nonnegative solutions of singular boundary value problems with sign changing nonlinearities, Comput. Math. Appl., 2003, 46, 1827–1837 http://dx.doi.org/10.1016/S0898-1221(03)90239-2[Crossref]
  • [5] Bartle R.G., A modern theory of integrations, AMS Providence, Rhode Island, 2001
  • [6] Berestycki H., Lions P.L., Peletier L.A., An ODE approach to the existence of positive solutions for semilinear problems in ℝN, Indiana Univ. Math. J., 1981, 30, 141–157 http://dx.doi.org/10.1512/iumj.1981.30.30012[Crossref]
  • [7] Bertsch M., Passo R.D., Ughi M., Discontinuous viscosity solutions of a degenerate parabolic equation, Trans. Amer. Math. Soc., 1990, 320, 779–798 http://dx.doi.org/10.2307/2001703[Crossref]
  • [8] Bertsch M., Ughi M., Positive properties of viscosity solutions of a degenerate parabolic equation, Nonlinear Anal., 1990, 14, 571–592 http://dx.doi.org/10.1016/0362-546X(90)90063-M[Crossref]
  • [9] Cabada A., Cid J.A., Extremal solutions of ϕ-Laplacian-diffusion scalar problems with nonlinear functional boundary conditions in a unified way, Nonlinear. Anal., 2005, 63, 2515–2524 http://dx.doi.org/10.1016/j.na.2004.09.031[Crossref]
  • [10] Cabada A., Nieto J.J., Extremal solutions of second order nonlinear periodic boundary value problems, Appl. Math. Comput., 1990, 40, 135–145 http://dx.doi.org/10.1016/0096-3003(90)90128-P[Crossref]
  • [11] Cabada A., Pouso R.P., Extremal solutions of strongly nonlinear discontinuous second-order equations with nonlinear functional boundary conditions, Nonlinear Anal., 2000, 42, 1377–1396 http://dx.doi.org/10.1016/S0362-546X(99)00158-3[Crossref]
  • [12] Carl S., Heikkilä S., Nonlinear differential equations in ordered spaces, Chapman & Hall/CRC, Monographs and Surveys in Pure and Applied Mathematics III, 2000
  • [13] Castro A., Sudhasree G., Uniqueness of stable and unstable positive solutions for semipositone problems, Nonlinear Anal., 1994, 22, 425–429 http://dx.doi.org/10.1016/0362-546X(94)90166-X[Crossref]
  • [14] Cherpion M., De Coster C., Habets P., Monotone iterative method for boundary value problem, Differential integral equations, 1999, 12, 309–338
  • [15] Cid J.A., On extremal fixed point in Schauder’s theorem with application to differential equations, Bull. Belg. Math. Soc. Simon Stevin, 2004, 11, 15–20
  • [16] Gidas B., Ni W.M., Nirenberg L., Symmetry of positive solutions of nonlinear elliptic equations in ℝN, Adv. Math., Suppl. Stud. 7A, 1981, 369–402
  • [17] Kelevedjiev P., Nonnegative solutions to some singular second-order boundary value problems, Nonlinear Anal., 1999, 36, 481–494 http://dx.doi.org/10.1016/S0362-546X(98)00025-X[Crossref]
  • [18] Kiguradze I., Some optimal conditions for solvability of two-point singular boundary value problems, Funct. Differ. Equ., 2003, 10, 259–281
  • [19] Kiguradze I.T., Shekhter B.L., Singular boundary value problems for second order ordinary differential equations, Itogi Nauki i Tekhniki. Ser. Sovrem. Probl. Mat. Nov. Dostizh., 1987, 30, 105–201 (in Russian), English translation: Journal of Soviet Mathematics, 1988, 43, 2340–2417
  • [20] Lang S., Real and functional analysis, Springer, New York, 1993
  • [21] O’Regan D., Existence of positive solutions to some singular and nonsingular second order boundary value problems, J. Differential Equations, 1990, 84, 228–251 http://dx.doi.org/10.1016/0022-0396(90)90077-3[Crossref]
  • [22] Rachůnková I., Singular mixed boundary value problem, J. Math. Anal. Appl., 2006, 320, 611–618 http://dx.doi.org/10.1016/j.jmaa.2005.07.037[Crossref]
  • [23] Rachůnková I., Staněk S., Connections between types of singularities in differential equations and smoothness of solutions for Dirichlet BVPs, Dyn. Contin. Discrete Impuls. Syst. Ser. A. Math. Anal., 2003, 10, 209–222
  • [24] Rachůnková I., Staněk S., Tvrdý M., Singularities and laplacians in boundary value problems for nonlinear differential equations, In: Cañada A., Drábek P., Fonda A. (Eds.), Handbook of differential equations, Ordinary differential equations, Vol. 3, 607–723, Elsevier, 2006
  • [25] Thompson H.B., Second order ordinary differential equations with fully nonlinear two point boundary conditions, Pacific J. Math., 1996, 172, 255–277
  • [26] Thompson H.B., Second order ordinary differential equations with fully nonlinear two point boundary conditions II, Pacific J. Math., 1996, 172, 259–297
  • [27] Wang J., Gao W., A note on singular nonlinear two-point boundary value problems, Nonlinear Anal., 2000, 39, 281–287 http://dx.doi.org/10.1016/S0362-546X(98)00165-5[Crossref]
  • [28] Zheng L., Su X., Zhang X., Similarity solutions for boundary layer flow on a moving surface in an otherwise quiescent fluid medium, Int. J. Pure Appl. Math., 2005, 19, 541–552

Typ dokumentu

Bibliografia

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