带梯度项的半线性椭圆方程整体解的存在性

By a sub-supersolution method and a perturbed argument,we show the existence of entire solutions for the semilinear elliptic problem-△u + a(x)|▽u|~q = λb(x)g(u),u 0,x ∈ R~N,lim(|x|→∞) u(x) = 0,where q ∈(1,2],λ 0,a and b are locally Holder continuous,a ≥0,b 0,(?)x∈ R~N,arid g ∈ C~1((0,∞),(0,∞)) which may be both possibly singular at zero and strongly unbounded at infinity.

Existence of Entire Solutions for Semilinear Elliptic Problems with Convection Terms

By a sub-supersolution method and a perturbed argument, we show the existence of entire solutions for the semilinear elliptic problem $- Delta u +a(x)|nabla u|^q=lambda b(x)g(u)$, $u>0$, $xin mathbb R^N$, $lim_{|x|rightarrow infty} u(x)=0$, where $qin (1,2]$, $lambda>0$, $a$ and $b$ are locally H"{o}lder continuous, $ageq 0$, $b>0$, $forall xin mathbb R^N$, and $gin C^1((0,infty), (0,infty))$ which may be both possibly singular at zero and strongly unbounded at infinity.