Solvability of multipoint bvps at resonance for various kernels

Abstract

in this paper, the Mawhin’s continuation theorem in the theory of coincidence degree has been used to investigate the existence of solutions for a class of nonlinear second-order differential systems of equations in Rⁿ associated with a multipoint boundary conditions at resonance. This is the first time thai a resonant boundary condition of multipoint with large dimension of the kernel has been considered. An example has also been provided to illustrate the result.