Two Positive Solutions of Third-Order BVP with Integral Boundary Condition and Sign-Changing Green's Function - Bing-Wei Niu; Jian-Ping Sun; Qiu-Yan Ren (Journal of Function Spaces)
We are concerned with the following third-order boundary value problem with integral boundary condition:   u′′′(t)=f(t,u(t)),  t∈[0,1],  u′(0)=u(1)=0,  u′′(η)+∫αβ‍u(t)dt=0, where 1/2<α≤β≤1,  α+β≤4/3, and η∈(1/2,α]. Although the corresponding Green's function is sign-changing, we still obtain the existence of at least two positive and decreasing solutions under some suitable conditions on f by using the two-fixed-point theorem due to Avery and Henderson. An example is also included to illustrate the main results obtained.