On critical exponents for the Pucci's extremal operators

 Access to full text

 Full (PDF)

1. [1] Cabré X., Caffarelli L.A., Fully Nonlinear Elliptic Equation, Colloquium Publication, 43, American Mathematical Society, 1995. Zbl0834.35002MR1351007
2. [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. Zbl0702.35085MR982351
3. [3] Chen W., Li C., Classification of solutions of some nonlinear elliptic equations, Duke Math. J.3 (3) (1991) 615-622. Zbl0768.35025MR1121147
4. [4] Clemons C., Jones C., A geometric proof of Kwong–Mc Leod uniqueness result, SIAM J. Math. Anal.24 (1993) 436-443. Zbl0779.35040MR1205535
5. [5] Coffman C., Uniqueness of the ground state solution for Δu−u+u3=0 and a variational characterization of other solutions, Arch. Rational Mech. Anal.46 (1972) 81-95. Zbl0249.35029
6. [6] Cutri A., Leoni F., On the Liouville property for fully nonlinear equations, Ann. Inst. H. Poincaré Analyse non lineaire17 (2) (2000) 219-245. Zbl0956.35035MR1753094
7. [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. Zbl0789.34025MR1215914
8. [8] Erbe L., Tang M., Structure of positive radial solutions of semilinear elliptic equation, J. Differential Equations133 (1997) 179-202. Zbl0871.34023MR1427849
9. [9] Gidas B., Symmetry and isolated singularitiesof positive solutions of nonlinear elliptic equations, in: Nonlinear Partial Differential Equations in Engineering and Applied Science (Proc. Conf., Univ. Rhode Island, Kingston, RI, 1979), Lecture Notes in Pure Appl. Math., 54, Dekker, New York, 1980, pp. 255-273. Zbl0444.35038MR577096
10. [10] Gidas B., Spruck J., Global and local behavior of positive solutions of nonlinear elliptic equations, Comm. Pure Appl. Math.34 (1981) 525-598. Zbl0465.35003MR615628
11. [11] Hale J., Ordinary Differential Equation, Wiley, New York, 1969. Zbl0186.40901
12. [12] Kajikiya R., Existence and asymptotic behavior of nodal solution for semilinear elliptic equation, J. Differential Equations106 (1993) 238-256. Zbl0791.35039MR1251853
13. [13] Kolodner I., The heavy rotating string – a nonlinear eigenvalue problem, Comm. Pure Appl. Math.8 (1955) 395-408. Zbl0065.17202MR71605
14. [14] Kwong M.K., Uniqueness of positive solution of Δu−u+up=0 in RN, Arch. Rational Mech. Anal.105 (1989) 243-266. Zbl0676.35032
15. [15] Kwong M.K., Zhang L., Uniqueness of positive solution of Δu+f(u)=0 in an annulus, Differential Integral Equations4 (1991) 583-596. Zbl0724.34023
16. [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. Zbl0581.35021
17. [17] Pohozaev S.I., Eigenfunctions of the equation Δu+λf(u)=0, Soviet Math.5 (1965) 1408-1411. Zbl0141.30202

1. Patricio L. Felmer, Alexander Quaas, Moxun Tang, Jianshe Yu, Monotonicity properties for ground states of the scalar field equation
2. Jérôme Busca, Maria J. Esteban, Alexander Quaas, Nonlinear eigenvalues and bifurcation problems for Pucci's operators
3. Patricio Felmer, Alexander Quaas, Moxun Tang, On the complex structure of positive solutions to Matukuma-type equations