Boundary behaviour for solutions of boundary blow-up problems in a borderline case

We investigate boundary blow-up solutions of the equation Δu=f(u) in a bounded domain Ω⊂RN under the condition that f(t) has a relatively slow growth as t goes to infinity. We show how the mean curvature of the boundary ∂Ω appears in the asymptotic expansion of the solution u(x) in terms of the distance of x from ∂Ω.

[1]  Alan C. Lazer,et al.  Asymptotic behavior of solutions of boundary blowup problems , 1994, Differential and Integral Equations.

[2]  Ahmed Mohammed,et al.  Existence and asymptotic behavior of blow-up solutions to weighted quasilinear equations , 2004 .

[3]  Second order estimates for boundary blow-up solutions of elliptic equations , 2007 .

[4]  Giovanni Porru,et al.  Asymptotic estimates and convexity of large solutions to semilinear elliptic equations , 1997 .

[5]  Florica-Corina St . Cand.  SOLUTIONS WITH BOUNDARY BLOW-UP FOR A CLASS OF NONLINEAR ELLIPTIC PROBLEMS , 2003 .

[6]  G. Porru,et al.  Second-order estimates for boundary blowup solutions of special elliptic equations , 2006 .

[7]  Serge Dumont,et al.  Back to the Keller-Osserman Condition for Boundary Blow-up Solutions , 2007 .

[8]  Robert Osserman,et al.  On the inequality $\Delta u\geq f(u)$. , 1957 .

[9]  Giovanni Porru,et al.  Problems for elliptic singular equations with a quadratic gradient term , 2007 .

[10]  D. Gilbarg,et al.  Elliptic Partial Differential Equa-tions of Second Order , 1977 .

[11]  Catherine Bandle,et al.  Boundary blow up for semilinear elliptic equations with nonlinear gradient terms , 1996, Advances in Differential Equations.

[12]  W. D. Evans,et al.  PARTIAL DIFFERENTIAL EQUATIONS , 1941 .

[13]  Catherine Bandle,et al.  Asymptotic behaviour of large solutions of quasilinear elliptic problems , 2003 .

[14]  C. Bandle,et al.  On second-order effects in the boundary behaviour of large solutions of semilinear elliptic problems , 1998, Differential and Integral Equations.

[15]  Corina Cîrstea,et al.  Nonlinear problems with boundary blow-up: a Karamata regular variation theory approach , 2005, Asymptot. Anal..

[16]  J. Keller.  On solutions of δu=f(u) , 1957 .

[17]  Vicentiu D. Rădulescu,et al.  Boundary blow-up in nonlinear elliptic equations of Bieberbach–Rademacher type , 2005, math/0506121.