On a class of Monge-Ampère type equations with lower order terms

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1. ALVINO, A. - FERONE, V. - TROMBETTI, G., On properties of some nonlinear eigenvalues, SIAM J. Math. Anal., 29, no. 2 (1998), 437-451. Zbl0908.35094MR1616519
2. BAKELMAN, I. J., Convex Analysis and nonlinear geometric elliptic equations, Springer-Verlag, 1994. Zbl0815.35001MR1305147
3. BELLONI, M. - KAWOHL, B., A direct uniqueness proof for equations involving the p-Laplace operator, Manuscripta Math., 109 (2) (2002), 229-231. Zbl1100.35032MR1935031
4. BRANDOLINI, B. - TROMBETTI, C., A symmetrization result for Monge-Ampère type equations, Preprint 2003. Zbl1189.35141MR2308477
5. BRANDOLINI, B. - TROMBETTI, C., Comparison results for Hessian equations via symmetrization, in preparation. Zbl1215.35067
6. BOCCARDO, L. - DRABEK, P. - GIACHETTI, D. - KUCERA, M., Generalization of Fredholm alternative for nonlinear differential operators, Nonlinear Analysis. T.M.A., 10 (10) (1986), 1083-1103. Zbl0623.34031MR857742
7. BREZIS, H. - OSWALD, L., Remarks on sublinear elliptic equations, Nonlinear Analysis T.M.A., 10 (1) (1986), 55-64. Zbl0593.35045MR820658
8. CAFFARELLI, L. A. - NIREMBERG, L. - SPRUCK, J., The Dirichlet problem for nonlinear second-order elliptic equations, Comm. Pure Appl. Math., 37 (1984), 369-402. Zbl0598.35047MR739925
9. CHENG, S. Y. - YAU, S. T., On the regularity of Monge-Ampère equation $det\left(\frac{{\partial }^{2}u}{\partial x_i\partial x_j}\right)=F\left(x,u\right)$, Comm. Pure Appl. Math., 30 (1977), 41-68. Zbl0347.35019MR437805
10. CHONG, K. M. - RICE, N. M., Equimeasurable rearrangements of functions, Queen's paper in pure and applied mathematics, n. 28. Zbl0275.46024
11. DIAZ, J. I. - SAA, J. E., Existence et unicité de solutions positives pour certaines équations elliptiques quasilinéaires, C. R. Acad. Sci. Paris, 305, Série I (1987), 521-524. Zbl0656.35039MR916325
12. FERONE, V. - MESSANO, B., A symmetrization result for nonlinear elliptic equations, to appear on Revista Mat. Complutense. Zbl1097.35049MR2083955
13. GILBARG, D. - TRUDINGER, N. S., Elliptic partial differential equations of second order, Springer-Verlag, 1983. Zbl0562.35001MR737190
14. KAWOHL, B., Rearrangements and convexity of the level sets in PDE, Springer-Verlag, Berlin (1985). Zbl0593.35002MR810619
15. KUTEV, N. D., Nontrivial solutions for the equations of Monge-Ampere type, J. Math. Anal. Appl., 132 (1988), 424-433. Zbl0658.35035MR943516
16. LINDQVIST, P., On the equation $\mathrm{div}\left({\left|\nabla u\right|}^{p-2}\nabla u\right)+\lambda {\left|u\right|}^{p-2}u=0$, Proceedings Amer. Math. Soc., 109 (1990), 157-164. Zbl0714.35029MR1007505
17. LIONS, P. L., Sur les equations de Monge-Ampère, Arch. Rat. Mech. Anal., 89 (1985), 93-122. Zbl0579.35027MR786541
18. LIONS, P. L., Two remarks on Monge-Ampère equations, Ann. Mat. Pura Appl., 142 (1985), 263-275. Zbl0594.35023MR839040
19. TALENTI, G., Some estimates of solutions to Monge-Ampère type equations in dimension two, Ann. scula Norm. sup. Pisa, (2) VII (1981), 183-230. Zbl0467.35044MR623935
20. TALENTI, G., Linear elliptic p.d.e.'s: level sets, rearrangements and a priori estimates of solutions, Boll. UMI, (6) 4-B (1985), 917-949. Zbl0602.35025MR831299
21. TRUDINGER, N. S., On new isoperimetric inequalities and symmetrization, J. Reine Angew. Math., 488 (1997), 203-220. Zbl0883.52006MR1465371
22. TSO, K., On symmetrization and hessian equations, J. Anal. Math., 52 (1989), 94-106. Zbl0675.35040MR981497
23. TSO, K., On a real Monge-Ampère functional, Invent. Math., 101 (1990), 425-448. Zbl0724.35040MR1062970
24. WANG, X. J., Existence of multiple solutions to the equations of Monge-Ampère type, J. Diff. Eq., 100 (1992), 95-118. Zbl0770.35019MR1187864
25. WANG, X. J., A class of fully nonlinear equations and related functionals, Indiana Univ. Math. J., 43 (1994), 25-54. Zbl0805.35036MR1275451