  Reaction-diffusion systems have been primary tools for studying pattern
formation. A skew-gradient system is well known to encompass a class of
activator-inhibitor type reaction-diffusion systems that exhibit localized
patterns such as fronts and pulses. While there is a substantial literature for
the case of a linear inhibitor equation, the study of nonlinear inhibitor
effect is still limited. To fill this research gap, we investigate standing
pulse solutions to a skew-gradient system in which both activator and inhibitor
reaction terms inherit nonlinear structures. Using a variational approach that
involves several nonlocal terms, we establish the existence of standing pulse
solutions with a sign change. In addition, we explore some qualitative
properties of the standing pulse solutions.
