完全非线性扰动方程的线性化原理

本文讨论方程u_i=a(t,εu,ε▽u,ε▽u)·▽u f(t,x,u,▽u)带第一初边值条件的解的存在性,其中a(t,0,0,0)>0,当|ξ|相似文献   

Multiplicity of solutions of weighted (p,q)-Laplacian with small source

In this article, we study the existence of infinitely many solutions to the degenerate quasilinear elliptic system-div(h_1(x)|▽u|~(p-2)▽u)=d(x)|u|~(r-2)u+G_u(x,u,v) in Ω,-div(h_2(x)|▽u|~(p-2)▽v)=f(x)|v|~(s-2)v + G_u(x,u,v) in Ω,u=v=0 on ■Ω where Ω is a bonded domain in R~N with smooth boundary ■Ω,N≥2,1 r p ∞,1 s q ∞; h_1(x) and h_2(x) are allowed to have "essential" zeroes at some points inΩ; d(x)|u|~(r-2)u and f(x)|v|~(s-2)v are small sources with Gu(x,u,v), Gv(x,u,v) being their high-order perturbations with respect to(u,v) near the origin, respectively.     

一类奇异拟线性椭圆方程正解的多重性

研究奇异拟线性椭圆型方程{-div(|x|~(-ap)|▽u|~(p-2)▽u) + f(x)|u|~(p-2) = g(x)\u|~(q-2)u + λh(x)|u|~(r-2),x R~N,u(x) 0,x∈ R~N,其中λ0是参数,1pN(N3),1rpgp*=0a(N—p)/p,p*=Np/{N~pd),aa+l,d=a+l-60,权函数f(x),g(x),h(x)满足一定的条件.利用山路引理和Ekeland变分原理证明了问题至少有两个非平凡的弱解.     

R~N上临界增长p-Kirchhoff型方程的非平凡解的存在性

本文主要研究以下具临界增长的非线性p-Kirchhoff型方程的非平凡解的存在性:{-(a+b∫_(R~N)|▽u|~p)?_pu=|u|~(p*-2)u+μf (x)|u|~(q-2)u, x∈R~N,(0.1) u∈D~(1,p)(R~N),其中a≥0,b0,1pN,1qp,p*=N_p/(N-p),μ≥0,?_pu=div(|▽u|~(p-2)▽u)表示p-Laplace算子对函数u的作用, f∈L(p*/(p*-q))(R~N)\{0}且f是非负的.本文利用Ekeland变分原理和山路定理证明方程(0.1)在适当条件下至少存在两个非平凡解.     

全空间上一类奇异p-Laplace方程无穷多解的存在性北大核心CSCD

本文研究了全空间上一类带奇异系数及其扰动的椭圆型p-Laplace问题-△_pu-μ(|u|^(p-2)u)/(|x|~p)=λ(u^(p*(t)-2))/(|x|~t)u+βf(x,u),x∈R^N,u∈D_0^(1,p)(R^N),其中N≥3,D_0^(1,p)(R^N)是C_0~∞(R^N)的闭包,△_pu=-div(|▽u|^(p-2)▽u),2     

一类Choquard型方程解的存在性

该文研究如下形式的Choquard型方程-△_pu+V(x)|u|~(p-2)u=(|x|~(-(N-α))*F(u))f(u),其中,-△_pu=div(|▽u|~(p-2)▽u)),x=(y,z)∈R~K×R~(N-K).假定混合位势V(y,z)关于y具有周期性,关于z具有强制性,并且非线性项f满足一定的条件,利用变分理论,该文证明了上述Choquard型方程具有山路水平解.     

全空间上一类奇异p-Laplace方程无穷多解的存在性

本文研究了全空间上一类带奇异系数及其扰动的椭圆型p-Laplace问题-△_pu-μ(|u|~(p-2)u)/(|x|~p)=λ(u~(p*(t)-2))/(|x|~t)u+βf(x,u),x∈R~N,u∈D_0~(1,p)(R~N),其中N≥3,D_0~(1,p)(R~N)是C_0~∞(R~N)的闭包,△_pu=-div(|▽u|~(p-2)▽u),2pN,0≤μμ=((N-p)~p)/(p~p),λ0,0≤tp,p~*(t)=(p(N-t))/(N-p)是Hardy-Sobolev临界指数.利用集中紧原理和极大极小化的方法,得到了在一定条件下该问题无穷多解的存在性.     

一类非齐次p-Kirchhoff型椭圆方程组多解的存在性

研究一类非齐次p-Kirchhoff型椭圆方程组{-M(∫RN|x|-ap|▽u|pdx)div(|x|-ap|▽u|p-2▽u)=α/α+βH(x)|u|α-2u|v|β+λh1(x)|u|q-2u+l1(x),-M(∫RN|x|-ap|▽v|pdx)div(|x|-ap|▽v|p-2▽v)=β/α+βH(x)|v|...     

全空间中带临界指数增长的Kirchhoff问题

本文考虑非齐次Kirchhoff型方程解的存在性与多解性:m(‖u‖N)(-ΔNu+V(x)|u|N-2u)=f(x,y)/|x|β+∈h(x),x∈RN,其中N≥2,‖u‖N=fRN(|▽u|N+V(x)|u|N)dx,ΔNu=div(|▽u|N-2▽u)是N-拉普拉斯算子,m:R+→R+表示Kirchhoff函数,...     

CORRECTION OF BILINEAR FINITE ELEMENT

Consider -△u=f in rectangle Ω, u=0 on Ω. Let u_h∈S_h be bilinear Galerkin projection of u. We proved the following: 1) superconvergence D_(xy)~2(u-u_h)=0(h~2Inh)|u|_(4,∞) at center Z_j of each rectangle element τ_j holds; 2) we can construct a piecewise linear contitnuous function w~h by D_(xy)~2u_h and define q_h∈S_h satisfying(▽q_h,▽v)=-1/3(h~2+k~2)(w~h,D_(xy)~2v),v∈S_h;3) correction _h=u_h+q_h are of high accuracy u-_h=0(h~4|Inh|~2)‖u‖_(4,∞);4) by _h the correction derivatives can be got such that Du-=0(h~3 |In h|~2)‖u‖~(4,∞).