On critical exponents for the Pucci's extremal operators

Annales de l'Institut Henri Poincare (C) Analyse Non Lineaire

Volumn 20, Issue 5, 2003, Pages 843-865

  Felmer, Patricio L ^a   Quaas, Alexander ^a  

^a UNIVERSITY OF CHILE   (Chile)

Author keywords

Critical exponents; Non divergence form operator; Positive radial solution; Pucci's operator

Indexed keywords

BOUNDARY CONDITIONS; LAPLACE TRANSFORMS; MATHEMATICAL OPERATORS; SET THEORY; THEOREM PROVING;

CRITICAL EXPONENTS; POSITIVE RADIAL SOLUTION;

NONLINEAR EQUATIONS;

EID: 0346724409     PISSN: 02941449     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0294-1449(03)00011-8     Document Type: Article

References (17)

1. Cabré X., Caffarelli L.A. Fully Nonlinear Elliptic Equation. Colloquium Publication. 43:1995;American Mathematical Society.
2. Caffarelli L., Gidas B., Spruck J. Asymptotic symmetry and local behavior of semilinear elliptic equations with critical Sobolev growth. Comm. Pure Appl. Math. 42:(3):1989;271-297.
3. Chen W., Li C. Classification of solutions of some nonlinear elliptic equations. Duke Math. J. 3:(3):1991;615-622.
4. Clemons C., Jones C. A geometric proof of Kwong-Mc Leod uniqueness result. SIAM J. Math. Anal. 24:1993;436-443.
5. 3 = 0 and a variational characterization of other solutions. Arch. Rational Mech. Anal. 46:1972;81-95.
6. Cutri A., Leoni F. On the Liouville property for fully nonlinear equations. Ann. Inst. H. Poincaré Analyse non lineaire. 17:(2):2000;219-245.
7. Deng Y., Cao D. Uniqueness of the positive solution for singular non-linear boundary value problems. Syst. Sci Math. Sci. 6:1993;25-31.
8. Erbe L., Tang M. Structure of positive radial solutions of semilinear elliptic equation. J. Differential Equations. 133:1997;179-202.
9. Gidas B. Symmetry and isolated singularitiesof positive solutions of nonlinear elliptic equations. Nonlinear Partial Differential Equations in Engineering and Applied Science (Proc. Conf., Univ. Rhode Island, Kingston, RI, 1979). Lecture Notes in Pure Appl. Math. 54:1980;255-273 Dekker, New York.
10. Gidas B., Spruck J. Global and local behavior of positive solutions of nonlinear elliptic equations. Comm. Pure Appl. Math. 34:1981;525-598.
11. Hale J. Ordinary Differential Equation. 1969;Wiley, New York.
12. Kajikiya R. Existence and asymptotic behavior of nodal solution for semilinear elliptic equation. J. Differential Equations. 106:1993;238-256.
13. Kolodner I. The heavy rotating string - a nonlinear eigenvalue problem. Comm. Pure Appl. Math. 8:1955;395-408.
14. N . Arch. Rational Mech. Anal. 105:1989;243-266.
15. Kwong M.K., Zhang L. Uniqueness of positive solution of Δu+f(u) = 0 in an annulus. Differential Integral Equations. 4:1991;583-596.
16. Ni W.M., Nussbaum R. Uniqueness and nonuniqueness for positive radial solutions of Δu+f(u,r) = 0 . Comm. Pure Appl. Math. 38:1985;67-108.
17. Pohozaev S.I. Eigenfunctions of the equation Δu+λf(u) = 0 . Soviet Math. 5:1965;1408-1411.