摘要
In this paper,the existence and multiplicity of positive solutions for a class of non-resonant fourth-order integral boundary value problem{u(4)(t)+βu″(t)-au(t)=f(t,u(t),u″(t)),t∈(0,1),u″(0)=u″(1)=0,u(0)=0,u(1)=(1/λ2-1/λ1)∫01q(s)f(s,u(s),u″(s))ds with two parameters are established by using the Guo-Krasnoselskii's fixedpoint theorem,where f∈C([0,1]×[0,+∞)×(-∞,0],[0,+∞)),q(t)∈L1[0,1]is nonnegative,α,β∈R and satisfyβ<2π2,α>0,α/π4+β/π2<1,λ1,2=(-β+√β^2+4a)/2.The corresponding examples are raised to demonstrate the results we obtained.
In this paper, the existence and multiplicity of positive solutions for a class of non-resonant fourth-order integral boundary value problem ■ with two parameters are established by using the Guo-Krasnoselskii’s fixedpoint theorem, where f ∈ C([0, 1] × [0, +∞) ×(-∞, 0], [0, +∞)), q(t) ∈ L1[0, 1]is nonnegative, α, β ∈ R and satisfy β < 2π2, α > 0, α/π4+ β/π2< 1, λ1,2=(-β ?■)/2. The corresponding examples are raised to demonstrate the results we obtained.
基金
Supported by the NSF of China(11761046)
