Abstract
For an open, bounded set Ω⊂RN, measurable bounded functions a(x),b(x) which are strictly positive and p,q>0, we prove the existence of a weak solution of the quasilinear b.v.p {−div[(a(x)+|u|q)∇u(x)]+b(x)u|u|p−1|∇u|2=f(x),x∈Ω;u(x)=0,x∈∂Ω. The datum f is assumed to be in L1(Ω) and does not satisfy any sign assumption.
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