奇异超线性二阶周期边值问题的正解

Positive Solutions to a Singular Superlinear Second Order Periodic Boundary Value Probelm

利用锥不动点定理证明一个二阶奇异周期边值问题- u″(t) +ρ2 u(t) =f(t,u(t) ) , 0≤ t≤ 2π,u(0 ) =u(2π) , u′(0 ) =u′(2π)正解的存在性 ,其中允许 f在 u=0处具有奇性 ,在 u=+∞处超线性 .

On the basis of the cone-fixed point theorem, the present paper deals with the existence of positive solutions to the superlinear second order periodic boundary value problem-u″(t)+ρ 2u(t)=f(t,u(t)), 0≤t≤2π, u(0)=u(2π), u′(0)=u′(2π)where f(t,u) is allowed to be singular at u=0 and superlinear at u=+∞.