Abstract
Existence and uniqueness results are obtained for positive radial solutions of a class of quasilinear elliptic equations in aN-ball or an annulus without monotone assumptions on the nonlinear termf. It is also proved that there is no non-radial positive solution.
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References
Guo Z M. Some existence and multiplicity results for a class of quasilinear elliptic eigenvalue problems. Nonlinear Anal, 1992, 18: 957–971
Guo Z M. Existence and uniqueness of positive radial solutions for a class of quasilinear elliptic equations. Appl Anal, 1992, 47: 173–190
Guo Z M, Webb J R L. Uniqueness of positive solutions for quasilinear elliptic equations when a parameter is large. Proc Royal Soc. Edinburgh, 1994, 124A: 189–198
Guo Z M. On the number of positive solutions for quasilinear elliptic eigenvalue problems. Nonlinear Anal., 1996, 27(2): 229–247
Guo Z M. On the positive solutions for a class of quasilinear non-positive problems. Chinese Quarterly J Math, 1996, 12: 1–11
Diaz J I. Nonlinear Partial Differential Equations and Free Boundaries. Vol. I. Elliptic Equations, in “Research Notes in Math”, 106, London: Pitman, 1985
Casas E, Fernandez A. Distributed control of systems governed by a general class of quasilinear elliptic equations. J Diff Eqns, 1993, 104: 20–47
Kichenassamy S. Quasilinear problems with singularities. Manuscripta Math, 1987, 57: 281–313
Kichenassamy S, Smoller J. On the existence of radial solutions of quasilinear elliptic equations. Nonlinearity, 1990, 3: 677–694
Ladyzhenskaya O, Uraltseva N. Linear and Quasilinear Elliptic Eqúations. New York, 1968
De Thelin F. Sur l'espace propre associe a la premiere valeur propre du pseudo-Laplacien’. C R Acad Sc Paris, Ser A, 1980, 303: 355–358
Tolksdorff P. On the Dirichlet problem for quasilinear equations in domains with conical boundary points'. Comm Partial Diff Eqns, 1983, 8(7): 773–817
Dancer E N. On the number of positive solutions of weakly nonlinear elliptic equations when a parameter is large. Proc London Math Soc, 1986, 53(3): 429–452
Gidas B, Ni W M, Nirenberg L. Symmetry and related properties via the maximum principle. Comm Math Phys, 1979, 68: 209–243
Gilbarg D, Trudinger N S. Elliptic Partial Differential Equations of Second Order. Springer-Verlag, 1977
Gidas B, Spruck J. A priori bounds for positive solutions of nonlinear elliptic equations. Comm Partial Diff Eqns, 1981, 6: 883–901.
Sattinger D H. Monotone methods in nonlinear elliptic and parabolic boundary value problems. Indiana Univ Math J, 1972, 21: 979–1000
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Supported by the Youth Foundations of National Education Commuttee and the Committee on Science and Technology of Henan Province
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Zongming, G., Zuodong, Y. Some uniqueness results for a class of quasilinear elliptic eigenvalue problems. Acta Mathematica Sinica 14, 245–260 (1998). https://doi.org/10.1007/BF02560211
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DOI: https://doi.org/10.1007/BF02560211