摘要
利用非线性增生映射值域的扰动定理 ,研究了非线性椭圆边值问题 ( @)在 L2 (Ω )中解的存在性 .( @) -△pu +g( x,u) =f a.e.在Ω中-〈v,| u|p- 2 u〉∈βx( u( x) ) a.e.在Γ上其中 f∈ L2 (Ω )给定 ,Ω RN,N 1 ,△ pu=div( | u|p- 2 u)为 P拉普拉斯算子 ,1 <p<+∞且 p>2 NN +1 ,v为 Γ的外法向导数 ,g:Ω× R→ R满足 Caratheodory条件 ,对 x∈ Γ,βx是正常、凸、下半连续函数 φx=φ( x,· )的次微分 ,其中 φ:Γ×R→ R.
By using the perturbation results on ranges of nonlinear accretive operators, we study the abstract results on the existence of a solution u∈L 2(Ω) of nonlinear boundary value problems(@) -△ pu+g(x,u)=fa.e. on Ω-<v,|u| p-2 u>∈β x(u(x))a.e. on Γwhere f∈L 2(Ω) is given, ΩR N, N1, △ pu=div(|u| p-2 u) represents the P-Laplacian operator, 1<p<+∞ and p>2NN+1, v denotes the exterior normal derivative to Γ, g:Ω×R→R satisfies Caratheodory′s conditions and for each x∈Γ, β x is the subdifferential of a suitably defined proper, convex, lower-semi-continuous function φ x=φ(x, ·) where φ:Γ×R→R.
出处
《数学的实践与认识》
CSCD
北大核心
2004年第1期123-130,共8页
Mathematics in Practice and Theory
