带Navier边值条件的 (p_(1),…,p_(n))双调和方程组多解性研究

Multiplicity results for a class of Navier boundary value systems with(p_(1),…,p_(n))-biharmonic operator

利用Ricceri的三临界点理论研究了带有Navier边值条件的(p_(1),…,p_(n))双调和方程组{Δ(|Δu_(i)|^( p i-2)Δu_(i))-α_(i)Δ_(p i) |u_(i)|+β_(i) u_(i) |^(p i-2) u_(i)=λF _(ui)(x,u_(1),…,u_(n)),x∈Ω,u_(i)=Δu_(i)=0,x∈∂Ω,弱解的存在性,得到了问题至少存在3个弱解的充分条件.

This paper studies the existence of multiplicity results for a class of Navier boundary value systems with(p_(1),…,p_(n))-biharmonic operator.{Δ(|Δu_(i)|^( p i-2)Δu_(i))-α_(i)Δ_(p i) |u_(i)|+β_(i) u_(i) |^(p i-2) u_(i)=λF _(ui)(x,u_(1),…,u_(n))+μG u_(i)(x,u_(1),…,u_(n)),inΩ,u_(i)=Δu_(i)=0,on∂Ω,Our technical approach is mainly based on a three critical points theorem.