<p>This paper investigates the pursuit-evasion problem involving one evader and multiple pursuers with limited sensing capability, where the evader tries to maximize the distance with the pursuers, while the pursuers have different objectives based on whether they can receive the information of the evader. The subgroup of pursuers who can observe the evader (called leaders) tries to be close to the evader, and the other subgroup of pursuers (called followers) tries to synchronize with their neighbors. When the subgraph formed by all leaders is complete, sufficient conditions are given to guarantee that the pursuers capture the evader and the pursuit-evasion game composed of the evader and leaders reaches Nash equilibrium. Furthermore, for the incomplete subgraph case, the distributed observers are proposed to estimate the relative positions between the evader and all leaders. It is shown that the distributed control strategy based on the observers converges exponentially to the Nash equilibrium solution, and makes the pursuers capture the evader. Finally, simulation examples are provided to verify the effectiveness of the proposed strategies.</p>