Second-order boundary estimates for large positive solutions to an elliptic system of competitive type
Keywords
Elliptic system, competitive type, second-order asymptotic behaviour, iteration methodAbstract
In this paper, we study the second-order boundary asymptotic behaviour for large positive solutions to an elliptic system of competitive type. First, we derive a second-order estimate to a related single weighted equation with boundary blow-up data. Then, by relaxing the system and iterating the estimate of the single equation, we establish second-order estimates of the solutions.References
C. Anedda and G. Porru, Second order estimates for boundary blow-up solutions of elliptic equations, Discrete Contin. Dyn. Syst. 2007, Dynamical Systems and Differential Equations, Proceedings of the 6th AIMS International Conference, Suppl. 54–63.
C. Anedda and G. Porru, Boundary estimates for solutions of weighted semilinear elliptic equations, Discrete Contin. Dyn. Syst. A 32 (2012), no. 11, 3801–3817.
C. Bandle and M. Marcus, On second-order effects in the boundary behaviour of large solutions of semilinear elliptic problems, Differential Integral Equations 11 (1998), 23–34.
M. Chuaqui, C. Cortázar, M. Elgueta and J. Garcı́a-Melián, Uniqueness and boundary behaviour of large solutions to elliptic problems with singular weights, Comm. Pure Appl. Anal. 3 (2004), 653–662.
M. Chuaqui, C. Cortázar, M. Elgueta, C. Flores, J. Garcı́a-Melián and R. Letelier, On an elliptic problem with boundary blow-up and a singular weight: The radial case, Proc. Roy. Soc. Edinburgh Sect. A 133 (2003), no. 6, 1283–1297.
M. Del Pino and R. Letelier, The influence of domain geometry in boundary blow-up elliptic problems, Nonlinear Anal. 48 (2002), 897–904.
J. Garcı́a-Melián, A remark on the existence of large solutions via sub and supersolutions, Electron. J. Differ. Equ. 110 (2003), 495–500.
J. Garcı́a-Melián, Uniqueness for boundary blow-up problems with continuous weights, Proc. Amer. Math. Soc. 135 (2007), 2785–2793.
E. Giarrusso and G. Porru, Second order estimates for boundary blow-up solutions of elliptic equations with an additive gradient term, Nonlinear Anal. 129 (2015), 160–172.
J. Garcı́a-Melián and J.D. Rossi, Boundary blow-up solutions to elliptic systems of competitive type, J. Differential Equations 206 (2004), 156–181.
S. Huang, Asymptotic behavior of boundary blow-up solutions to elliptic equations, Z. Angew. Math. Phys. 67 (2016), no. 1, 3 pp.
S. Huang, Q. Tian, S. Zhang, et al, A second-order estimate for blow-up solutions of elliptic equations, Nonlinear Anal. 74 (2011), 2342–2350.
B. Khamessi, Existence and asymptotic behavior of positive blow up solutions for semilinear elliptic coupled system, J. Math. Phys. 60 (2019), no. 9, 091505.
B. Khamessi and S.B. Othman, Exact boundary behavior of positive large solutions of a nonlinear Dirichlet problem, Nonlinear Anal. 187 (2019), 307-319.
A.V. Lair, A.W. Wood, Large solutions of semilinear elliptic problems, Nonlinear Anal. 37 (1999), 805–812.
C. Mu, S. Huang, Q. Tian, et al., Large solutions for an elliptic system of competitive type: Existence, uniqueness and asymptotic behavior, Nonlinear Anal. 71 (2009), 4544–4552.
L. Wei and Z. Yang, Large solutions of quasilinear elliptic system of competitive type: existence and asymptotic behavior, Int. J. Differ. Equ. 1 (2010), 1–17.
Z. Zhang, The second expansion of large solutions for semilinear elliptic equations, Nonlinear Anal. 74 (2011), 3445–3457.
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