## On blow up solutions of a quasilinear elliptic equation.(English)Zbl 0954.35066

The existence and asymptotic behaviour of the solutions of the equation $$\Delta u + |Du|^q =f(u)$$ in a bounded and regular domain in $${\mathbb{R}}^N$$ which diverge on $$\partial \Omega$$, is studied.

### MSC:

 35J65 Nonlinear boundary value problems for linear elliptic equations 35B40 Asymptotic behavior of solutions to PDEs

### Keywords:

blow up solutions; elliptic equations
Full Text:

### References:

 [1] Amman, Indiana Univ. Math. J. 27 pp 779– (1978) [2] Bandle, C. R. Acad. Sci. Paris 18 pp 455– (1994) [3] Bandle, Symposia Mathematica 35 pp 93– (1994) [4] Bandle, Advances in Differential Equations 1 pp 133– (1996) [5] Bandle, Boll. U. M. I. 11-B pp 227– (1997) [6] Bandle, J. d’Anal. Math. 58 pp 9– (1992) [7] Bandle, Ann. Inst. H. Poincaré 12 pp 155– (1995) [8] Bandle, WSSIA 3 pp 59– (1994) [9] Chipot, Siam J. Math. Anal. 20 pp 886– (1989) [10] and : Elliptic Partial Differential Equations of Second Order, Springer-Verlag, Berlin-Heidelberg-New York-Tokyo [11] Kazdan, Commun. Pure and Appl. Math. 31 pp 619– (1989) [12] Keller, Commun. Pure and Appl. Math. 10 pp 503– (1957) [13] Lasry, Math. Ann. 283 pp 583– (1989) [14] Lazer, Diff. and Int. Eqns. 7 pp 1001– (1994) [15] Ossermann, Pac. J. Math. 7 pp 1641– (1957) · Zbl 0083.09402
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.