Uniqueness of Radial Solutions for Elliptic Equation Involving the Pucci Operator ()
Abstract
The solution of a nonlinear elliptic equation involving Pucci maximal operator and super linear nonlinearity is studied. Uniqueness results of positive radial solutions in the annulus with Dirichlet boundary condition are obtained. The main tool is Lane-Emden transformation and Koffman type analysis. This is a generalization of the corresponding classical results involving Laplace operator.
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Y. Liu, "Uniqueness of Radial Solutions for Elliptic Equation Involving the Pucci Operator," Advances in Pure Mathematics, Vol. 2 No. 6, 2012, pp. 408-412. doi: 10.4236/apm.2012.26061.
Conflicts of Interest
The authors declare no conflicts of interest.
References
|
[1]
|
D. Gilbarg and N. S. Trudinger, “Elliptic Partial Differential Equations of Second Order,” Springer-Verlag, Berlin, 2001.
|
|
[2]
|
L. A. Caffarelli and X. Cabre, “Fully Nonlinear Elliptic Equations,” American Mathematical Society Colloquium Publications, Providence, 1995.
|
|
[3]
|
D. A. Labutin, “Removable Singularities for Fully Non- linear Elliptic Equations,” Archive for Rational Mechanics and Analysis, Vol. 155, No. 3, 2000, pp. 201-214.
|
|
[4]
|
P. L. Felmer and A. Quaas, “Critical Exponents for Uniformly Elliptic Extremal Operators,” Indiana University Mathematics Journal, Vol. 55, No. 2, 2006, pp. 593-629.
|
|
[5]
|
P. L. Felmer and A. Quaas, “On Critical Exponents for the Pucci’s Extremal Operators,” Annales de l’Institut Henri Poincare, Vol. 20, No. 5, 2003, pp. 843-865.
|
|
[6]
|
W. M. Ni and R. D. Nussbaum, “Uniqueness and Non-uniqueness for Positive Radial Solutions of
△u+f(u,r)=0,” Communications on Pure and Applied Mathematics, Vol. 38, No. 1, 1985, pp. 67-108.
|