We investigate the bi-harmonic problem{Δ^(2)u-α▽·(f(▽u))-βΔ_(p)u=g(x,u) in Ω,δu/δn=0,δ(Δu)/δn=0 on δΩ,where Δ^(2)u=Δ(Δu),Δ_(p)u=div(|▽u|^(p-2)▽u)with p>2.Ω is a bounded smooth domain in R^...We investigate the bi-harmonic problem{Δ^(2)u-α▽·(f(▽u))-βΔ_(p)u=g(x,u) in Ω,δu/δn=0,δ(Δu)/δn=0 on δΩ,where Δ^(2)u=Δ(Δu),Δ_(p)u=div(|▽u|^(p-2)▽u)with p>2.Ω is a bounded smooth domain in R^(N),N≥1.By using a special function space with the constraint ∫_(Ω)udx=0,under suitable assumptions on f and g(x,u),we show the existence and multiplicity of sign-changing solutions to the above problem via the Mountain pass theorem and the Fountain theorem.Recent results from the literature are extended.展开更多
We consider the existence of a nontrivial solution for the Dirichlet boundary value problem -△u+a(x)u=g(x,u),in Ω u=0, on Ω We prove an abstract result on the existence of a critical point for the functional f on a...We consider the existence of a nontrivial solution for the Dirichlet boundary value problem -△u+a(x)u=g(x,u),in Ω u=0, on Ω We prove an abstract result on the existence of a critical point for the functional f on a Hilbert space via the local linking theorem. Different from the works in the literature, the new theorem is constructed under the(C)* condition instead of (PS)* condition.展开更多
In this paper,we consider a class of quasilinear Schrodinger-Poisson problems of the form∫-(a+b∫_(R)^(N)|■μ|^(2)dx)■μ+V(x)u+Фu-1/2u■(u^(2))-λ|u|^(p-2)u=0 in R^(N),-ΔФ=u^(2),u(x)→0,|x|→∞in R^(N),∫_(R)^(N...In this paper,we consider a class of quasilinear Schrodinger-Poisson problems of the form∫-(a+b∫_(R)^(N)|■μ|^(2)dx)■μ+V(x)u+Фu-1/2u■(u^(2))-λ|u|^(p-2)u=0 in R^(N),-ΔФ=u^(2),u(x)→0,|x|→∞in R^(N),∫_(R)^(N)|u|^(p)dx=1,where a>0,b≥0,N≥3,λappears as a Lagrangian multiplier,and 4<p<2·2^(*)=4N/N-2.We deal with two different cases simultaneously,namely lim|x|→∞V(x)=1 and limjxj!1 V(x)=V1.By using the method of invariant sets of the descending flow combined with the genus theory,we prove the existence of infinitely many sign-changing solutions.Our results extend and improve some recent work.展开更多
文摘We investigate the bi-harmonic problem{Δ^(2)u-α▽·(f(▽u))-βΔ_(p)u=g(x,u) in Ω,δu/δn=0,δ(Δu)/δn=0 on δΩ,where Δ^(2)u=Δ(Δu),Δ_(p)u=div(|▽u|^(p-2)▽u)with p>2.Ω is a bounded smooth domain in R^(N),N≥1.By using a special function space with the constraint ∫_(Ω)udx=0,under suitable assumptions on f and g(x,u),we show the existence and multiplicity of sign-changing solutions to the above problem via the Mountain pass theorem and the Fountain theorem.Recent results from the literature are extended.
文摘We consider the existence of a nontrivial solution for the Dirichlet boundary value problem -△u+a(x)u=g(x,u),in Ω u=0, on Ω We prove an abstract result on the existence of a critical point for the functional f on a Hilbert space via the local linking theorem. Different from the works in the literature, the new theorem is constructed under the(C)* condition instead of (PS)* condition.
基金supported by Shandong Natural Science Foundation of China(Grant No.ZR2020MA005).
文摘In this paper,we consider a class of quasilinear Schrodinger-Poisson problems of the form∫-(a+b∫_(R)^(N)|■μ|^(2)dx)■μ+V(x)u+Фu-1/2u■(u^(2))-λ|u|^(p-2)u=0 in R^(N),-ΔФ=u^(2),u(x)→0,|x|→∞in R^(N),∫_(R)^(N)|u|^(p)dx=1,where a>0,b≥0,N≥3,λappears as a Lagrangian multiplier,and 4<p<2·2^(*)=4N/N-2.We deal with two different cases simultaneously,namely lim|x|→∞V(x)=1 and limjxj!1 V(x)=V1.By using the method of invariant sets of the descending flow combined with the genus theory,we prove the existence of infinitely many sign-changing solutions.Our results extend and improve some recent work.
