Geodesic
Nonexistence of entire positive solution for a conformal $k$-Hessian inequality
Czechoslovak Mathematical Journal, Tome 70 (2020) no. 2, pp. 311-322
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In this paper, we study the nonexistence of entire positive solution for a conformal $k$-Hessian inequality in $\mathbb {R}^n$ via the method of proof by contradiction.
In this paper, we study the nonexistence of entire positive solution for a conformal $k$-Hessian inequality in $\mathbb {R}^n$ via the method of proof by contradiction.
DOI : 10.21136/CMJ.2019.0289-18
Classification : 35B08, 35B09, 35J60
Keywords: conformal Hessian inequality; entire positive solution 
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Jiang, Feida; Cui, Saihua; Li, Gang. Nonexistence of entire positive solution for a conformal $k$-Hessian inequality. Czechoslovak Mathematical Journal, Tome 70 (2020) no. 2, pp. 311-322. doi: 10.21136/CMJ.2019.0289-18

[1] Aubin, T.: Équations différentielles non linéaires et problème de Yamabe concernant la courbure scalaire. J. Math. Pur. Appl., IX. Sér. 55 (1976), 269-296 French. | MR | JFM

[2] Aubin, T.: Problèmes isopérimétriques et espaces de Sobolev. J. Diff. Geom. 11 (1976), 573-598 French. | DOI | MR | JFM

[3] Bao, J., Ji, X., Li, H.: Existence and nonexistence theorem for entire subsolutions of $k$-Yamabe type equations. J. Differ. Equations 253 (2012), 2140-2160. | DOI | MR | JFM

[4] Brezis, H.: Semilinear equations in $\mathbb{R}^N$ without condition at infinity. Appl. Math. Optimization 12 (1984), 271-282. | DOI | MR | JFM

[5] Caffarelli, L., Gidas, B., Spruck, J.: Asymptotic symmetry and local behavior of semilinear elliptic equations with critical Sobolev growth. Commun. Pure Appl. Math. 42 (1989), 271-297. | DOI | MR | JFM

[6] Caffarelli, L., Nirenberg, L., Spruck, J.: The Dirichlet problem for nonlinear second order elliptic equations III: Functions of the eigenvalues of the Hessian. Acta Math. 155 (1985), 261-301. | DOI | MR | JFM

[7] Gidas, B., Spruck, J.: Global and local behavior of positive solutions of nonlinear elliptic equations. Commun. Pure Appl. Math. 34 (1981), 525-598. | DOI | MR | JFM

[8] Ji, X., Bao, J.: Necessary and sufficient conditions on solvability for Hessian inequalities. Proc. Am. Math. Soc. 138 (2010), 175-188. | DOI | MR | JFM

[9] Jiang, F., Trudinger, N. S.: Oblique boundary value problems for augmented Hessian equations I. Bull. Math. Sci. 8 (2018), 353-411. | DOI | MR | JFM

[10] Jiang, F., Trudinger, N. S., Yang, X.-P.: On the Dirichlet problem for a class of augmented Hessian equations. J. Differ. Equations 258 (2015), 1548-1576. | DOI | MR | JFM

[11] Jin, Q., Li, Y., Xu, H.: Nonexistence of positive solutions for some fully nonlinear elliptic equations. Methods Appl. Anal. 12 (2005), 441-449. | DOI | MR | JFM

[12] Keller, J. B.: On solutions of $\Delta u=f(u)$. Commun. Pure Appl. Math. 10 (1957), 503-510. | DOI | MR | JFM

[13] Li, A., Li, Y. Y.: On some conformally invariant fully nonlinear equations II: Liouville, Harnack and Yamabe. Acta Math. 195 (2005), 117-154. | DOI | MR | JFM

[14] Lieberman, G. M.: Second Order Parabolic Differential Equations. World Scientific Publishing, Singapore (1996). | DOI | MR | JFM

[15] Loewner, C., Nirenberg, L.: Partial differential equations invariant under conformal or projective transformations. Contributions to Analysis: A Collection of Papers Dedicated to Lipman Bers Academic Press, New York (1974), 245-272. | MR | JFM

[16] Osserman, R.: On the inequality $\Delta u\ge f(u)$. Pac. J. Math. 7 (1957), 1641-1647. | DOI | MR | JFM

[17] Ou, Q.: Nonexistence results for Hessian inequality. Methods Appl. Anal. 17 (2010), 213-224. | DOI | MR | JFM

[18] Ou, Q.: Singularities and Liouville theorems for some special conformal Hessian equations. Pac. J. Math. 266 (2013), 117-128. | DOI | MR | JFM

[19] Ou, Q.: A note on nonexistence of conformal Hessian inequalities. Adv. Math., Beijing 46 (2017), 154-158. | MR | JFM

[20] Schoen, R.: Conformal deformation of a Riemannian metric to constant scalar curvature. J. Differ. Geom. 20 (1984), 479-495. | DOI | MR | JFM

[21] Sheng, W., Trudinger, N. S., Wang, X.-J.: The $k$-Yamabe problem. Surv. Differ. Geom. 17 (2012), 427-457. | DOI | MR | JFM

[22] Trudinger, N. S.: Remarks concerning the conformal deformation of Riemannian structures on compact manifolds. Ann. Sc. Norm. Super. Pisa, Sci. Fis. Mat., III. Ser. 22 (1968), 265-274. | MR | JFM

[23] Trudinger, N. S.: Recent developments in elliptic partial differential equations of Monge-Ampère type. International Congress of Mathematicians. Vol. III European Mathematical Society, Zürich (2006), 291-302. | DOI | MR | JFM

[24] Viaclovsky, J. A.: Conformal geometry, contact geometry, and the calculus of variations. Duke Math. J. 101 (2000), 283-316. | DOI | MR | JFM

[25] Yamabe, H.: On a deformation of Riemannian structures on compact manifolds. Osaka Math. J. 12 (1960), 21-37. | MR | JFM

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