Boundary-value Problems at Resonance with Three Dimensional Kernels
نویسندگان
چکیده
In this article, we consider the boundary-value problem x′′′(t) = f(t, x(t), x′(t), x′′(t)), t ∈ (0, 1), x′′(0) = m X i=1 αix (ξi), x ′(0) = l X k=1 γkx (σk), x(1) = n X j=1 βjx(ηj), where f : [0, 1] × R3 → R is a Carathéodory 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.
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