SOLUTIONS TO THIRD-ORDER MULTI-POINT BOUNDARY-VALUE PROBLEMS AT RESONANCE WITH THREE DIMENSIONAL KERNELS

作者：Li, Shuang; Yin, Jian; Du, Zengji^*

来源：Electronic Journal of Differential Equations, 2014.

• Multi-point boundary-value problem
• coincidence degree theory
• resonance

In this article, we consider the boundary-value problem
x'"/(t) - f (t, x(t), x' (t), x" (t)), t is an element of (0, 1),
x"(0) - (m)Sigma(i=1) alpha ix" (xi i), x'(0) - (l)Sigma(k=1) gamma kx'(sigma(k)), x(1) - (n)Sigma(j=1) beta(j)x(eta(j)),
where f : [0, 1] x R-3 -> R is a Caratheodory function, and the kernel to the linear operator has dimension three. Under some resonance conditions, by using the coincidence degree theorem, we show the existence of solutions. An example is given to illustrate our results.

• 出版日期2014-3-5
• 单位中国矿业大学（北京）