关键词: 高阶边值问题, 对称正解, 五个泛函, Sturm-Liouville

Abstract:

In this paper, the authors consider the following higher order Sturm-Liouville-type four-point boundary value problem

{u^(2m)(t)=f(t, u(t), u'(t), … , u^{(2m-1)(t)),
 u^{(2i)(0)-αu⁽²ⁱ⁺¹⁾(ξ)=0, u^(2i)}(1)+αu⁽²ⁱ⁺¹⁾(η)=0, 0≤ i ≤ m-1, 
where nonlinear f depends on all lower order derivatives of u. Sufficient conditions of existence of at least three symmetric positive solutions are established by applying five-functional fixed point theorem.

Key words: Higher-order boundary value problem, Symmetric positive solution, Five-functional, Sturm-Liouville-type