Back to the Keller-Osserman condition for boundary blow-up solutions. (English) Zbl 1137.35030
The paper is concerned with the study of the existence, uniqueness and numerical approximation of boundary blow-up solutions for elliptic partial differential equations \(\Delta u=f(u)\), where \(f\) satisfies the so-called Keller-Osserman condition. As an example, an infinite family of boundary blow-up solutions for equation \(\Delta u=u^2(1+\cos u)\) is constructed on a ball.
Reviewer: Nicolae Pop (Baia Mare)
MSC:
| 35J60 | Nonlinear elliptic equations |
| 35J67 | Boundary values of solutions to elliptic equations and elliptic systems |
| 65N06 | Finite difference methods for boundary value problems involving PDEs |
References:
| [1] | Bandle, Large solutions of semilinear elliptic equations : existence uniqueness and asymptotic behavior, Math Anal 58 pp 9– (1992) · Zbl 0802.35038 · doi:10.1007/BF02790355 |
| [2] | Gidas, Symmetry and related properties via the maxi - mum principle, Math Phy 68 pp 209– (1979) · Zbl 0425.35020 · doi:10.1007/BF01221125 |
| [3] | Osserman, On the inequality u f u Pacific, Math 7 pp 1641– (1957) · Zbl 0083.09402 |
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