In this paper, we establish fountain theorems over cones and apply it to the quasilinear elliptic problem{-△Pu=λ｜u｜q-2u＋μ｜u｜ y-2u,x∈Ω,u=0,x∈δΩ to show that problem （1） possesses infinitely many solution...In this paper, we establish fountain theorems over cones and apply it to the quasilinear elliptic problem{-△Pu=λ｜u｜q-2u＋μ｜u｜ y-2u,x∈Ω,u=0,x∈δΩ to show that problem （1） possesses infinitely many solutions, where 1 〈 p 〈 N, 1 〈 q 〈 P 〈 γ, Ω∩→ R^N is a smooth bounded domain and λ, μ∈ R.展开更多
The existence of high energy periodic solutions for the second-order Hamiltonian system -ü（t）＋A（t）u（t）=▽F（t,u（t）） with convex and concave nonlinearities is studied, where F（t, u） = F1（t,u）＋F2（t,...The existence of high energy periodic solutions for the second-order Hamiltonian system -ü（t）＋A（t）u（t）=▽F（t,u（t）） with convex and concave nonlinearities is studied, where F（t, u） = F1（t,u）＋F2（t,u）. Under the condition that F is an even functional, infinitely many solutions for it are obtained by the variant fountain theorem. The result is a complement for some known ones in the critical point theory.展开更多
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
基金supported by ARC grant of Australiasupported by National Natural Sciences Foundations of China (10961016 and 10631030)NSF of Jiangxi(2009GZS0011)
文摘In this paper, we establish fountain theorems over cones and apply it to the quasilinear elliptic problem{-△Pu=λ｜u｜q-2u＋μ｜u｜ y-2u,x∈Ω,u=0,x∈δΩ to show that problem （1） possesses infinitely many solutions, where 1 〈 p 〈 N, 1 〈 q 〈 P 〈 γ, Ω∩→ R^N is a smooth bounded domain and λ, μ∈ R.
文摘The existence of high energy periodic solutions for the second-order Hamiltonian system -ü（t）＋A（t）u（t）=▽F（t,u（t）） with convex and concave nonlinearities is studied, where F（t, u） = F1（t,u）＋F2（t,u）. Under the condition that F is an even functional, infinitely many solutions for it are obtained by the variant fountain theorem. The result is a complement for some known ones in the critical point theory.
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.
