含临界参数及临界指数的非线性双调和方程的多解问题(英文)

By using variational method, the multiplicity of solutions for nonlinear biharmonic equation involving critical parameter and critical exponent are established.     

一类含临界指数双调和方程变号解的存在性

本文运用一个新的环绕定理讨论了一类含临界指数双调和方程分别在Navier和Dirichlet边界下变号解的存在性.     

MULTIPLE AND SIGN-CHANGING SOLUTIONS FOR NONLINEAR ELLIPTIC EQUATION WITH CRITICAL POTENTIAL AND CRITICAL PARAMETER

Some embedding inequalities in Hardy-Sobolev space are proved.Furthermore,by the improved inequalities and the linking theorem,in a new k-order Sobolev-Hardy space,we obtain the existence of sign-changing solutions for the nonlinear elliptic equation {-△(k)u:=-△u-(((N-2)2)/4)U/︱X︱2-1/4 sum from i=1 to(k-1) u/(︱x︱2(In(i)R/︱x︱2))=f(x,u),x ∈Ω,u=0,x ∈Ω,where 0 ∈ΩBa(0)RN,N≥3,ln(i)=i éj=1 ln(j),and R=ae(k-1),where e(0)=1,e(j) = ee(j-1) for j≥1,ln(1)=ln,ln(j)=ln ln(j-1) for j≥2.Besides,positive andnegative solutions are obtained by a variant mountain pass theorem.     

具临界位势和权函数的非线性双调和问题

本文考虑具有临界位势和临界权函数的四维非线性重调和问题,证明非平凡解的存在性.