Nonlinear eigenvalues and bifurcation problems for Pucci's operators

 Access to full text

 Full (PDF)

1. [1] Bardi M., Da Lio F., Propagation of maxima and strong maximum principle for viscosity solution of degenerate elliptic equation I: convex operators, Nonlinear Anal.44 (2001) 991-1006. Zbl1135.35342MR1829815
2. [2] Bensoussan A., Lions J.L., Applications of Variational Inequalities in Stochastic Control, Stud. Math. Appl. 12, North-Holland, Amsterdam, 1982, Translated from the French. Zbl0478.49002MR653144
3. [3] Berestycki H., On some nonlinear Sturm–Liouville problems, J. Differential Equations26 (3) (1977) 375-390. Zbl0331.34020MR481230
4. [4] Berestycki H., Nirenberg L., On the method of moving planes and the sliding method, Boll. Soc. Brasil Mat. (N.S.)22 (1991) 237-275. Zbl0784.35025MR1159383
5. [5] Berestycki H., Nirenberg L., Varadhan S.R.S., The principal eigenvalue and maximum principle for second-order elliptic operators in general domains, Comm. Pure Appl. Math.47 (1) (1994) 47-92. Zbl0806.35129MR1258192
6. [6] Cabré X., Caffarelli L.A., Fully Nonlinear Elliptic Equation, Amer. Math. Soc. Colloq. Publ., vol. 43, Amer. Math. Soc., 1995. Zbl0834.35002MR1351007
7. [7] Caffarelli L., Kohn J.J., Nirenberg L., Spruck J., The Dirichlet problem for nonlinear second order elliptic equations II, Comm. Pure Appl. Math.38 (1985) 209-252. Zbl0598.35048MR780073
8. [8] Crandall M., Ishi H., Lions P.L., User's guide to viscosity solutions of second order partial differential equations, Bull. Amer. Math. Soc.27 (1) (1992). Zbl0755.35015MR1118699
9. [9] Crandall M.G., Kocan M., Świech A., $L^p$ theory for fully nonlinear uniformly parabolic equations, Comm. Partial Differential Equations25 (11&12) (2000) 1997-2053. Zbl0973.35097MR1789919
10. [10] Dancer E.N., On the Dirichlet problem for weakly non-linear elliptic partial differential equations, Proc. Roy. Soc. Edinburgh Sect. A76 (4) (1976/77) 283-300. Zbl0351.35037MR499709
11. [11] del Pino M., Elgueta M., Manásevich R., A homotopic deformation along pof a Leray–Schauder degree result and existence for ${\left({\left|u^{\text{'}}\right|}^{p-2}{u}^{\text{'}}\right)}^{\text{'}}+f\left(t\text{,}u\right)=0$, $u\left(0\right)=u\left(T\right)=0$, $pgt;1$, J. Differential Equations80 (1) (1989) 1-13. Zbl0708.34019MR1003248
12. [12] del Pino M., Manásevich R., F. Global bifurcation from the eigenvalues of the p-Laplacian, J. Differential Equations92 (2) (1991) 226-251. Zbl0781.35017MR1120904
13. [13] Drábek P., Solvability and Bifurcations of Nonlinear Equations, Pitman Res. Notes Math. Ser., vol. 264, Longman Scientific and Technical, Harlow, 1992, copublished in the United States with John Wiley and Sons, New York, 1992. Zbl0753.34002MR1175397
14. [14] Felmer P., Quaas A., Critical exponents for the Pucci's extremal operators, C. R. Acad. Sci. Paris, Ser. I335 (2002) 909-914. Zbl1032.35069MR1952548
15. [15] Felmer P., Quaas A., On critical exponents for the Pucci's extremal operators, Ann Inst. H. Poicaré Anal. Non Linéaire20 (5) (2003) 843-865. Zbl1274.35115MR1995504
16. [16] Felmer P., Quaas A., Positive solutions to ‘semilinear’ equation involving the Pucci's operator, J. Differential Equations199 (2004) 376-393. Zbl1070.34032
17. [17] de Figueiredo D., Gossez J.P., On the first curve of the Fučik spectrum of an elliptic operator, Differential Integral Equations7 (5–6) (1994) 1285-1302. Zbl0797.35032MR1269657
18. [18] Fučík S., Solvability of Nonlinear Equations and Boundary Value Problems, Math. Appl., vol. 4, Reidel, 1980, With a foreword by Jean Mawhin. Zbl0453.47035MR620638
19. [19] Gallouet T., Kavian O., Résultats d'existence et de non-existence pour certains problemes demi-linéaires a l'infini, (in French. English summary), Ann. Fac. Sci. Toulouse Math.5 (3–4) (1981) 201-246. Zbl0495.35001MR658734
20. [20] Gilbarg D., Trudinger N.S., Elliptic Partial Differential Equation of Second Order, Springer-Verlag, 1983. Zbl0562.35001MR737190
21. [21] Lions P.L., Bifurcation and optimal stochastic control, Nonlinear Anal.2 (1983) 177-207. MR688774
22. [22] Lions P.L., Optimal control of diffusion processes and Hamilton–Jacobi–Bellman equations. I. The dynamic programming principle and applications, Comm. Partial Differential Equations8 (10) (1983) 1101-1174. Zbl0716.49022MR709164
23. [23] Lions P.L., Optimal control of diffusion processes and Hamilton–Jacobi–Bellman equations. II. Viscosity solutions and uniqueness, Comm. Partial Differential Equations8 (11) (1983) 1229-1276. Zbl0716.49023MR709162
24. [24] Lions P.L., Optimal control of diffusion processes and Hamilton–Jacobi–Bellman equations. III. Regularity of the optimal cost function, in: Nonlinear Partial Differential Equations and Their Applications. Collège de France seminar, vol. V (Paris, 1981/1982), 1983, pp. 95-205. Zbl0716.49024MR725360
25. [25] Lions P.L., A remark on Bony maximum principle, Proc. Amer. Math. Soc.88 (3) (1983) 503-508. Zbl0525.35028MR699422
26. [26] Lions P.L., Two remarks on Monge–Ampère equations, Ann. Mat. Pura Appl.142 (4) (1985) 263-275. Zbl0594.35023MR839040
27. [27] Ni W.M., Nussbaum R., Uniqueness and nonuniqueness for positive radial solutions of $\Delta u+f\left(u\text{,}r\right)=0$, Comm. Pure Appl. Math.38 (1985) 67-108. Zbl0581.35021MR768105
28. [28] Pucci C., Operatori ellittici estremanti, Ann. Mat. Pure Appl.72 (1966) 141-170. Zbl0154.12402MR208150
29. [29] Pucci C., Maximum and minimum first eigenvalue for a class of elliptic operators, Proc. Amer. Math. Soc.17 (1966) 788-795. Zbl0149.07601MR199576
30. [30] Quaas A., Existence of positive solutions to a ‘semilinear’ equation involving the Pucci's operator in a convex domain, Differential Integral Equations17 (2004) 481-494. Zbl1174.35373
31. [31] Rabinowitz P.H., Some aspect of nonlinear eigenvalue problem, Rocky Moutain J. Math.74 (3) (1973) 161-202. Zbl0255.47069MR320850
32. [32] Rabinowitz P.H., Some global results for nonlinear eigenvalue problems, J. Funct. Anal.7 (1971) 487-513. Zbl0212.16504MR301587
33. [33] P.H. Rabinowitz, Théorie du degré topologique et applications à des problèmes aux limites non linéaires, Lectures Notes Lab. Analyse Numérique Université PARIS VI, 1975. 
34. [34] E. Rouy, First semi-eigenvalue for nonlinear elliptic operator, preprint. Zbl0764.65052
35. [35] Safonov M.V., On the classical solution of Bellman elliptic equation, Soviet Math. Dokl.30 (1984). Zbl0595.35011
36. [36] Schechter M., The Fučík spectrum, Indiana Univ. Math. J.43 (4) (1994) 1139-1157. Zbl0833.35050MR1322614

1. Stefania Patrizi, The principal eigenvalue of the ∞-laplacian with the Neumann boundary condition
2. Stefania Patrizi, The principal eigenvalue of the ∞-Laplacian with the Neumann boundary condition