Large solutions of semilinear elliptic equations with nonlinear gradient terms
1999 ◽
Vol 22
(4)
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pp. 869-883
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Keyword(s):
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.
2016 ◽
Vol 40
(7)
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pp. 2596-2609
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Keyword(s):
2005 ◽
Vol 73
(1)
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pp. 221-236
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1987 ◽
Vol 40
(5)
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pp. 623-657
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1986 ◽
Vol 104
(2)
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pp. 291-306
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1982 ◽
pp. 133-155
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