<p>This paper focuses on the nonemptiness and boundedness of the solution sets for split equilibrium problems in reflexive Banach spaces. Based on the recession theory, we establish the equivalent characterizations on the nonemptiness and boundedness of the solution sets with pseudomonotonicity. When (weak) coercivity conditions hold, we provide sufficient conditions to guarantee the nonemptiness and boundedness of the solution sets without pseudomonotonicity. As an application, we investigate stability analysis for split equilibrium problems, when both the mapping and the constraint set are perturbed by different parameters.</p>