Boundary behavior of large solutions to elliptic equations with nonlinear gradient terms

2012 ◽  
Vol 64 (4) ◽  
pp. 1283-1304
Author(s):  
Ling Mi ◽  
Bin Liu
Keyword(s):  
Elliptic Equations ◽  
Boundary Behavior ◽  
Large Solutions

scholarly journals Large solutions of semilinear elliptic equations with nonlinear gradient terms

1999 ◽  
Vol 22 (4) ◽  
pp. 869-883 ◽  
Author(s):  
Alan V. Lair ◽  
Aihua W. Wood
Keyword(s):  
Positive Solutions ◽  
Compact Support ◽  
Elliptic Equations ◽  
Nonnegative Function ◽  
Semilinear Elliptic Equations ◽  
Decay Condition ◽  
Large Solutions ◽  
Semilinear Elliptic ◽  
The Given

We show that large positive solutions exist for the equation(P±):Δu±|∇u|q=p(x)uγinΩ⫅RN(N≥3)for appropriate choices ofγ>1,q>0in which the domainΩis either bounded or equal toRN. The nonnegative functionpis continuous and may vanish on large parts ofΩ. IfΩ=RN, thenpmust satisfy a decay condition as|x|→∞. For(P+), the decay condition is simply∫0∞tϕ(t)dt<∞, whereϕ(t)=max|x|=tp(x). For(P−), we require thatt2+βϕ(t)be bounded above for some positiveβ. Furthermore, we show that the given conditions onγandpare nearly optimal for equation(P+)in that no large solutions exist if eitherγ≤1or the functionphas compact support inΩ.

scholarly journals Uniqueness and boundary behavior of large solutions to elliptic problems with singular weights

2004 ◽  
Vol 3 (4) ◽  
pp. 653-662 ◽  
Author(s):  
M. Chuaqui ◽  
◽  
C. Cortázar ◽  
M. Elgueta ◽  
J. García-Melián ◽  
...  
Keyword(s):  
Boundary Behavior ◽  
Elliptic Problems ◽  
Large Solutions ◽  
Singular Weights
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