The paper considers an -point boundary value problem for a higher-order differential equation of the form
where and are continuous functions. Further, , are two integers, , , , . The authors study the problem at resonance because they assume that
Moreover, they do not need that all ’s, , have the same sign.
The authors prove a new existence result under certain sign and growth conditions imposed on . The growth of in some variables can be superlinear. The proofs are based on Mawhin’s continuation theorem. Some examples illustrate the obtained result.