Existence and asymptotic behavior of strictly convex solutions for singular k-Hessian equations with nonlinear gradient terms

References

[1] R. Alsaedi, H. Mâagli and N. Zeddini, Exact behavior of the unique positive solution to some singular elliptic problem in exterior domains, Nonlinear Anal. 119 (2015), 186–198. 10.1016/j.na.2014.09.018Suche in Google Scholar

[2] C. Budd, M. C. Knaap and L. A. Peletier, Asymptotic behavior of solutions of elliptic equations with critical exponents and Neumann boundary conditions, Proc. Roy. Soc. Edinburgh Sect. A 117 (1991), no. 3–4, 225–250. 10.1017/S0308210500024707Suche in Google Scholar

[3] L. Caffarelli, L. Nirenberg and J. Spruck, The Dirichlet problem for nonlinear second-order elliptic equations. I. Monge–Ampère equation, Comm. Pure Appl. Math. 37 (1984), no. 3, 369–402. 10.1002/cpa.3160370306Suche in Google Scholar

[4] M. Feng, Convex solutions of Monge–Ampère equations and systems: Existence, uniqueness and asymptotic behavior, Adv. Nonlinear Anal. 10 (2021), no. 1, 371–399. 10.1515/anona-2020-0139Suche in Google Scholar

[5] M. Feng, H. Sun and X. Zhang, Strictly convex solutions for singular Monge–Ampère equations with nonlinear gradient terms: existence and boundary asymptotic behavior, Partial Differ. Equ. Appl. 1 (2020), no. 5, Paper No. 27. 10.1007/s42985-020-00025-zSuche in Google Scholar

[6] M. Feng and X. Zhang, On a k-Hessian equation with a weakly superlinear nonlinearity and singular weights, Nonlinear Anal. 190 (2020), Article ID 111601. 10.1016/j.na.2019.111601Suche in Google Scholar

[7] B. Guan, The Dirichlet problem for a class of fully nonlinear elliptic equations, Comm. Partial Differential Equations 19 (1994), no. 3–4, 399–416. 10.1080/03605309408821022Suche in Google Scholar

[8] J. Han, Time-dependent tug-of-war games and normalized parabolic p-Laplace equations, Nonlinear Anal. 214 (2022), Paper No. 112542. 10.1016/j.na.2021.112542Suche in Google Scholar

[9] S. Huang, Asymptotic behavior of boundary blow-up solutions to elliptic equations, Z. Angew. Math. Phys. 67 (2016), no. 1, Article ID 3. 10.1007/s00033-015-0606-ySuche in Google Scholar

[10] H. Jian, Hessian equations with infinite Dirichlet boundary value, Indiana Univ. Math. J. 55 (2006), no. 3, 1045–1062. 10.1512/iumj.2006.55.2728Suche in Google Scholar

[11] H. Jian and Y. Li, Optimal boundary regularity for a singular Monge–Ampère equation, J. Differential Equations 264 (2018), no. 11, 6873–6890. 10.1016/j.jde.2018.01.051Suche in Google Scholar

[12] J. Karamata, Sur un mode de croissance régulière. Théorèmes fondamentaux, Bull. Soc. Math. France 61 (1933), 55–62. 10.24033/bsmf.1196Suche in Google Scholar

[13] A. C. Lazer and P. J. McKenna, On a singular nonlinear elliptic boundary-value problem, Proc. Amer. Math. Soc. 111 (1991), no. 3, 721–730. 10.1090/S0002-9939-1991-1037213-9Suche in Google Scholar

[14] A. C. Lazer and P. J. McKenna, On singular boundary value problems for the Monge–Ampère operator, J. Math. Anal. Appl. 197 (1996), no. 2, 341–362. 10.1006/jmaa.1996.0024Suche in Google Scholar

[15] C. Liu, Existence and boundary behavior of solutions for boundary blow-up quasilinear elliptic problems with gradient terms, Differ. Equ. Appl. 13 (2021), no. 3, 281–295. 10.7153/dea-2021-13-16Suche in Google Scholar

[16] S. I. Resnick, Extreme Values, Regular Variation, and Point Processes, Appl. Probab. 4, Springer, New York, 1987. 10.1007/978-0-387-75953-1Suche in Google Scholar

[17] J. Sánchez, Asymptotic behavior of solutions of a k-Hessian evolution equation, J. Differential Equations 268 (2020), no. 4, 1840–1853. 10.1016/j.jde.2019.09.028Suche in Google Scholar

[18] E. Seneta, Regularly Varying Functions, Lecture Notes in Math. 508, Springer, Berlin, 1976. 10.1007/BFb0079658Suche in Google Scholar

[19] H. Sun and M. Feng, Boundary behavior of k-convex solutions for singular k-Hessian equations, Nonlinear Anal. 176 (2018), 141–156. 10.1016/j.na.2018.06.010Suche in Google Scholar

[20] N. V. Thin, Multiplicity and concentration of solutions to a fractional ( p , p 1 ) -Laplace problem with exponential growth, J. Math. Anal. Appl. 506 (2022), no. 2, Paper No. 125667. 10.1016/j.jmaa.2021.125667Suche in Google Scholar

[21] H. Wan, Y. Shi and X. Qiao, Entire large solutions to the k-Hessian equations with weights: Existence, uniqueness and asymptotic behavior, J. Math. Anal. Appl. 503 (2021), no. 1, Paper No. 125301. 10.1016/j.jmaa.2021.125301Suche in Google Scholar

[22] X. J. Wang, A class of fully nonlinear elliptic equations and related functionals, Indiana Univ. Math. J. 43 (1994), no. 1, 25–54. Suche in Google Scholar

[23] J. Yuan and Z. Yang, Existence and boundary behavior of positive solutions of quasi-linear elliptic singular equations with a gradient term, J. Partial Differ. Equ. 27 (2014), no. 4, 318–332. 10.4208/jpde.v27.n4.3Suche in Google Scholar

[24] L. Zhang, Z. Yang, G. Wang and D. Baleanu, Existence and asymptotic behavior of solutions of a class of k-Hessian equation, Acta Math. Sci. Ser. A (Chinese Ed.) 41 (2021), no. 5, 1357–1371. Suche in Google Scholar

[25] X. Zhang, On a singular k-Hessian equation, Appl. Math. Lett. 97 (2019), 60–66. 10.1016/j.aml.2019.05.019Suche in Google Scholar

[26] X. Zhang, Analysis of nontrivial radial solutions for singular superlinear k-Hessian equations, Appl. Math. Lett. 106 (2020), Article ID 106409. 10.1016/j.aml.2020.106409Suche in Google Scholar

[27] X. Zhang and Y. Du, Sharp conditions for the existence of boundary blow-up solutions to the Monge–Ampère equation, Calc. Var. Partial Differential Equations 57 (2018), no. 2, Paper No. 30. 10.1007/s00526-018-1312-3Suche in Google Scholar

[28] X. Zhang and M. Feng, Boundary blow-up solutions to the k-Hessian equation with a weakly superlinear nonlinearity, J. Math. Anal. Appl. 464 (2018), no. 1, 456–472. 10.1016/j.jmaa.2018.04.014Suche in Google Scholar

[29] X. Zhang and M. Feng, Boundary blow-up solutions to the k-Hessian equation with singular weights, Nonlinear Anal. 167 (2018), 51–66. 10.1016/j.na.2017.11.001Suche in Google Scholar

[30] X. Zhang and M. Feng, The existence and asymptotic behavior of boundary blow-up solutions to the k-Hessian equation, J. Differential Equations 267 (2019), no. 8, 4626–4672. 10.1016/j.jde.2019.05.004Suche in Google Scholar

[31] Z. Zhang, Large solutions of semilinear elliptic equations with a gradient term: Existence and boundary behavior, Commun. Pure Appl. Anal. 12 (2013), no. 3, 1381–1392. 10.3934/cpaa.2013.12.1381Suche in Google Scholar

[32] Z. Zhang, Boundary behavior of large solutions to p-Laplacian elliptic equations, Nonlinear Anal. Real World Appl. 33 (2017), 40–57. 10.1016/j.nonrwa.2016.05.008Suche in Google Scholar

[33] Z. Zhang, Large solutions to the Monge–Ampère equations with nonlinear gradient terms: existence and boundary behavior, J. Differential Equations 264 (2018), no. 1, 263–296. 10.1016/j.jde.2017.09.010Suche in Google Scholar

[34] Z. Zhang, Optimal global and boundary asymptotic behavior of large solutions to the Monge–Ampère equation, J. Funct. Anal. 278 (2020), no. 12, Article ID 108512. 10.1016/j.jfa.2020.108512Suche in Google Scholar

[35] Z. Zhang, Optimal global asymptotic behavior of the solution to a singular Monge–Ampère equation, Commun. Pure Appl. Anal. 19 (2020), no. 2, 1129–1145. 10.3934/cpaa.2020053Suche in Google Scholar

[36] Z. Zhang and B. Li, The boundary behavior of the unique solution to a singular Dirichlet problem, J. Math. Anal. Appl. 391 (2012), no. 1, 278–290. 10.1016/j.jmaa.2012.02.010Suche in Google Scholar