帶對流項的一類次線性橢圓型方程正整體解的存在性.pdf

1、煙臺大學(xué)碩士學(xué)位論文帶對流項的一類次線性橢圓型方程正整體解的存在性姓名：薛洪濤申請學(xué)位級別：碩士專業(yè)：應(yīng)用數(shù)學(xué)指導(dǎo)教師：張志軍20070501煙 臺 大 學(xué) 碩 士 學(xué) 位 論 文ABSTRACTBy a sub-supersolution method, a perturbation argument and the maximum princi-ple, combining with the theory of estimates

2、and regularity of second order linear ellipticdifferential equations, we study the following nonlinear elliptic problems: ? ? ? ?? ? ???u = p(x)[g(u) + f(u) + λ|?u|q], u > 0, x ∈ RN,u(x) → 0, 當(dāng) |x| → ∞.Here, N ≥ 1, q

3、∈ (0, 2], λ ∈ R and λ ?= 0. Also we assume that g ∈ C1((0, ∞), (0, ∞))satisfying limu→0+ g(u)u = +∞ and limu→∞ g(u)u = 0, f : [0, ∞) → [0, ∞) is locallyH¨ older continuous and satisfies limu→0+ f(u)u = +∞ and limu→∞

4、 f(u)u = 0. Moreover,p ∈ Cα loc(RN) (α ∈ (0, 1)) and p(x) > 0, ? x ∈ RN.We respectively show the existence of positive entire solutions for the above nonlin-ear elliptic problem in two cases: λ > 0 and λ < 0.KEY