Existence of standing pulse solutions to a skew-gradient system

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 that exhibit localized patterns such as fronts and pulses. While there substantial literature the case linear inhibitor equation, study nonlinear effect still limited. To fill this research gap, we investigate standing pulse solutions in which both activator reaction terms inherit structures. Using variational approach involves several nonlocal terms, establish existence with sign change. In addition, explore some qualitative properties solutions.