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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)



On a singular quasilinear anisotropic elliptic boundary value problem

Authors: Y. S. Choi, A. C. Lazer and P. J. McKenna
Journal: Trans. Amer. Math. Soc. 347 (1995), 2633-2641
MSC: Primary 35J65; Secondary 35J70
MathSciNet review: 1277103
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Abstract: We consider the problem

$\displaystyle {u^a}{u_{xx}} + {u^b}{u_{yy}} + p({\mathbf{x}}) = 0$

with $ a \geqslant 0$, $ b \geqslant 0$, on a smooth convex bounded region in $ {{\mathbf{R}}^2}$ with Dirichlet boundary conditions. We show that if the positive function $ p$ is uniformly bounded away from zero, then the problem has a classical solution.

References [Enhancements On Off] (What's this?)

  • [1] S. Čanić, and B. L. Keyfitz, An elliptic problem arising from the unsteady transonic small disturbance equation, preprint.
  • [2] M. G. Crandall, P. H. Rabinowitz, and L. Tartar, On a Dirichlet problem with a singular nonlinearity, Comm. Partial Differential Equations 2 (1977), 193-222. MR 0427826 (55:856)
  • [3] D. Gilbarg and N. S. Trudinger, Elliptic partial differential equations of second order, 2nd ed., Springer-Verlag, 1983. MR 737190 (86c:35035)
  • [4] A. C. Lazer and P. J. McKenna, On a singular nonlinear elliptic boundary value problem, Proc. Amer. Math. Soc. 111 (1991), 721-730. MR 1037213 (91f:35099)
  • [5] A. Nachman and A. Callegari, A nonlinear singular boundary value problem in the theory of pseudoplastic fluids, SIAM J. Appl. Math. 28 (1986), 271-281.
  • [6] C A. Stuart, Existence theorems for a class of nonlinear integral equations, Math. Z. 137 (1974), 49-66. MR 0348416 (50:914)
  • [7] S. D. Taliaferro, A nonlinear singular boundary value problem, Nonlinear Analysis TMA 3 (1979), 897-904. MR 548961 (81i:34011)

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Keywords: Subsolution, supersolution, singular
Article copyright: © Copyright 1995 American Mathematical Society

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