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One-dimensional boundary blow up problem with a nonlocal term (2405.18846v2)
Published 29 May 2024 in math.AP
Abstract: In this paper, we study a nonlocal boundary blow up problem on an interval and obtain the precise asymptotic formula for solutions when the bifurcation parameter in the problem is large.
- Comput. Math. Appl., 49, (2005), pp.85–93.
- C. Bandle, and M. Marcus: “Large” solutions of semilinear elliptic equations: existence, uniqueness and asymptotic behavior, J. Anal. Math., 58, (1992), pp.9–24.
- C. Bandle, and M. Marcus: Asymptotic behavior of solutions and their derivatives for semilinear elliptic problems with blowup on the boundary, Ann. Inst. H. Poincaré Anal. Non Linéaire., 12(2) (1995), pp.155–171.
- Advanced Nonlinear Studies, 7 (2007), pp.271–298.
- J.B. Keller: On solutions of Δu=f(u)Δ𝑢𝑓𝑢\Delta u=f(u)roman_Δ italic_u = italic_f ( italic_u ), Comm. Pure Appl. Math., 10 (1957), pp.503–510.
- S. Kim: A note on boundary blow-up problem of Δu=upΔ𝑢superscript𝑢𝑝\Delta u=u^{p}roman_Δ italic_u = italic_u start_POSTSUPERSCRIPT italic_p end_POSTSUPERSCRIPT, Bull. Korean Math. Soc., 56 (2019), pp.245–251.
- D. A. Labutin: Wiener regularity for large solutions of nonlinear equations, Ark. Mat., 41(2) (2003), pp.307–339.
- A. C. Lazer, and P. J. McKenna: Asymptotic behavior of solutions of boundary blowup problems, Differential Integral Equations, 7(3-4) (1994), pp.1001–1019.
- M. Marcus, and L. Véron: Uniqueness and asymptotic behavior of solutions with boundary blow-up for a class of nonlinear elliptic equations, Ann. Inst. H. Poincaré Anal. Non Linéaire., 14(2) (1997), pp.237–274.
- M. Marcus, and L. Véron: Existence and uniqueness results for large solutions of general nonlinear elliptic equations, J. Evol. Equations, 3(4) (2004), pp.637–652.
- R. Osserman: On the inequality Δu≥f(u)Δ𝑢𝑓𝑢\Delta u\geq f(u)roman_Δ italic_u ≥ italic_f ( italic_u ), Pacific J. Math., 7 (1957), pp.1641–1647.
- T. Shibata: Global and asymptotic behaviors of bifurcation curves of one-dimensional nonlocal elliptic equations, J.Math.Anal.Appl.516 (2022)
- L. Véron: Generalized boundary value problems for nonlinear elliptic equations, In: Proceedings of the USA-Chile Workshop on Nonlinear Analysis (Viña del Mar-Valparaiso, 2000). Electron. J. Differ. Equ. Conf. 6, pp.313–342.
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