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Global bifurcation of sign-changing radial solutions of elliptic equations of order 2m in annular domains

  • Received: 10 May 2020 Accepted: 25 May 2020 Published: 03 June 2020
  • MSC : 35J40, 35G30, 34B27, 47H11

  • In this paper we study the global bifurcation of sign-changing radial solutions for some semilinear elliptic problems of order 2m in an annulus with Dirichlet boundary conditions.

    Citation: Ruyun Ma, Dongliang Yan, Liping Wei. Global bifurcation of sign-changing radial solutions of elliptic equations of order 2m in annular domains[J]. AIMS Mathematics, 2020, 5(5): 4909-4916. doi: 10.3934/math.2020313

    Related Papers:

  • In this paper we study the global bifurcation of sign-changing radial solutions for some semilinear elliptic problems of order 2m in an annulus with Dirichlet boundary conditions.



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    [1] C. V. Coffman, M. Marcus, Existence and uniqueness results for semilinear Dirichlet problems in annuli, Arch. Rational Mech. Anal., 108 (1989), 293-307. doi: 10.1007/BF01041066
    [2] L. H. Erbe, H. Wang, On the existence of positive solutions of ordinary di fferential equations, Proc. Amer. Math. Soc., 120 (1994), 743-748. doi: 10.1090/S0002-9939-1994-1204373-9
    [3] L. H. Erbe, S. C. Hu, H. Wang, Multiple positive solutions of some boundary value problems, J. Math. Anal. Appl., 184 (1994), 640-648. doi: 10.1006/jmaa.1994.1227
    [4] K. Lan, J. R. L. Webb, Positive solutions of semilinear di fferential equations with singularities, J. Differential Equations, 148 (1998), 407-421. doi: 10.1006/jdeq.1998.3475
    [5] S. S. Lin, F. M. Pai, Existence and multiplicity of positive radial solutions for semilinear elliptic equations in annular domains, Siam J. Math. Anal., 22 (1991), 1500-1515. doi: 10.1137/0522097
    [6] H. Wang, On the existence of positive solutions for semilinear elliptic equations in the annulus, J. Differential Equations, 109 (1994), 1-7. doi: 10.1006/jdeq.1994.1042
    [7] R. Dalmasso, Elliptic equations of order 2m in annular domains, Trans. Amer. Math. Soc., 347 (1995), 3575-3585.
    [8] R. Ma, B. Thompson, Nodal solutions for nonlinear eigenvalue problems, Nonlinear Anal., 59 (2004), 707-718. doi: 10.1016/j.na.2004.07.030
    [9] E. N. Dancer, On the structure of solutions of non-linear eigenvalue problems, Indiana Univ. Math. J., 23 (1973/74), 1069-1076.
    [10] U. Elias, Eigenvalue problems for the equation Ly + λp(x)y = 0, J. Differential Equations, 29 (1978), 28-57.
    [11] B. P. Rynne, Global bifurcation for 2mth-order boundary value problems and infinitely many solutions of superlinear problems, J. Differential Equations, 188 (2003), 461-472. doi: 10.1016/S0022-0396(02)00146-8
    [12] M. A. Naimark, Elementary theory of linear di fferential operators, New York: Ungar, 1967.
    [13] W. A. Coppel, Disconjugacy, Lectures Notes in Math, New York: Springer-Verlag, 1971.
    [14] U. Elias, Oscillation Theory of Two-Term Di fferential Equations, Mathematics and Its Applications, The Netherlands, Dordrecht: Kluwer Academic Publishers, 1997.
    [15] P. H. Rabinowitz, Some global results for nonlinear eigenvalue problems, J. Funct. Anal., 7 (1971), 487-513. doi: 10.1016/0022-1236(71)90030-9
    [16] P. Drábek, G. Holubová, Positive and negative solutions of one-dimensional beam equation, Appl. Math. Lett., 51 (2016), 1-7. doi: 10.1016/j.aml.2015.06.019
    [17] A. Cabada, R. R. Enguiça, Positive solutions of fourth order problems with clamped beam boundary conditions, Nonlinear Anal., 74 (2011), 3112-3122. doi: 10.1016/j.na.2011.01.027
    [18] R. Ma, H. Wang, M. Elsanosi, Spectrum of a linear fourth-order di fferential operator and its applications, Math. Nachr., 286 (2013), 1805-1819. doi: 10.1002/mana.201200288
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