A THIRD ORDER NONLOCAL BOUNDARY VALUE PROBLEM AT RESONANCE

作者：Kaufmann Eric R^*

来源：Electronic Journal of Qualitative Theory of Differential Equations, 2009, (16): 1-11.

DOI：10.14232/ejqtde.2009.4.16

• Coincidence degree theory
• nonlocal boundary value problem
• resonance

We consider the third-order nonlocal boundary value problem
u'''(t) = f(t, u(t)), a.e. in (0, 1),
u(0) = 0, u'(rho) = 0,
u ''(1) = lambda[u ''],
where 0 < rho < 1, the nonlinear term f satisfies Caratheodory conditions with respect to L(1)[0, T], lambda[v] = integral(1)(0)v(t)d Lambda(t), and the functional lambda satisfies the resonance condition lambda[1] = 1. The existence of a solution is established via Mawhin's coincidence degree theory.

• 出版日期2009