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Uniqueness of positive solutions of a quasilinear Dirichlet problem with exponential nonlinearity

Published online by Cambridge University Press:  14 November 2011

Adimurthi
Adimurthi
Affiliation:
TIFR Centre, P.B. 1234, Bangalore-560012, India, e-mail: aditi@math.tifrbng.res.in
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Abstract

Uniqueness of positive solutions of the following equation:

has been obtained, where B ⊂ ℝn is the ball of unit radius and λ > 0. Moreover, if n = 2, then the solutions are nondegenerate.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 128 , Issue 5 , 1998 , pp. 895 - 906
Copyright
Copyright © Royal Society of Edinburgh 1998

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References

1Adimurthi, and Yadava, S. L.. An elementary proof of the uniqueness of positive radial solutions of a quasilinear Dirichlet problem. Arch. Rational Mech. Anal. 127 (1994), 219–29.CrossRefGoogle Scholar
2Atkinson, F. V. and Peletier, L. A.. Ground states and Dirichlet problems for –;∆u = f(u) in ℝ2. Arch. Rational Mech. Anal. 98 (1988), 147–65.Google Scholar
3Budd, C. and Norbury, J.. Semilinear elliptic equations and super critical growth. J. Differential Equations 68 (1987), 169–97.CrossRefGoogle Scholar
4Kesavan, S. and Pacella, F.. Symmetry of positive solutions of a quasilinear elliptic equation via isoperimetric inequalities. Appl. Anal. 54 (1994), 27–37.CrossRefGoogle Scholar
5Kwong, M. K. and Li, Y.. Uniqueness of radial solutions of semilinear elliptic equations. Trans. Amer. Math. Soc. 333 (1992), 339–63.CrossRefGoogle Scholar
6Liquin, Z.. Uniqueness of positive solutions of ∆u + u + u p = 0 in a finite ball. Comm. Partial Differential Equations 17 (1992), 1141–64.Google Scholar
7Ni, W. M. and Nussbaum, R. D.. Uniqueness and non-uniqueness for positive radial solutions of ∆u + f(u, r) = 0. Comm. Pure Appl. Math. 38 (1985), 171–85.CrossRefGoogle Scholar
8Srikanth, P. N.. Uniqueness of solutions of nonlinear Dirichlet problems. Differential Integral Equations 7 (1993), 663–70.Google Scholar