对非线性椭圆边值问题解的存在性的研究

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 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.

Study of the Existence of the Solution of Nonlinear Elliptic Boundary Value Problems

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-∈β x(u(x))a.e. on Γwhere f∈L 2(Ω) is given, ΩR N, N1, △ pu=div(|u| p-2 u) represents the P-Laplacian operator, 12NN+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.