一類半線性橢圓方程組Robin問題正解的先驗估計和存在性.pdf

1、湖南大學碩士學位論文一類半線性橢圓方程組Robin問題正解的先驗估計和存在性姓名：李量夫申請學位級別：碩士專業(yè)：應(yīng)用數(shù)學指導教師：戴求億20070521一類半線性橢圓方程組 Robin 問題正解的先驗估計和存在性 IIIAbstract In this paper, we are concerned with the question of existence of a pair of smooth functions ( ) u x

2、 and ( ) v x satisfying the following system: 0,, 0,, 0, 0, ,0 , ,qp u v xv u xu v xu v u v x n n α β?? + = ∈? ?? + = ∈? ? ? ? > > ∈? ? ? ? ? + = = + ∈?? ? ? ? ? ? ?Where , , , 0 p q α β >

3、; are positive constants, 1 1 1, 1 1np q n? + ≥ + +n ? is the outward unit normal on ?? , n ?∈? is a smooth bounded domain. We firstly establish priori estimates for 1 pq > and 1 pq < ; After that we prove the

4、existence result: The system has a classical positive solution 2, 2, ( , ) ( ) ( ) r r u v C C ∈ ? × ? , supposing , p q satisfies some conditions; At the end we have some useful theorems for general semi-l