In recent years, continuous improvements in SAR resolution have significantly benefited applications such as urban monitoring and target detection. However, the improvement in resolution leads to increased discrepancies in scattering characteristics, posing challenges to the generalization ability of target detection models. While domain adaptation technology is a potential solution, the inevitable discrepancies caused by resolution differences often lead to blind feature adaptation and unreliable semantic propagation, ultimately degrading the domain adaptation performance. To address these challenges, this paper proposes a novel SAR target detection method (termed CR-Net), that incorporates structure priors and evidential learning theory into the detection model, enabling reliable domain adaptation for cross-resolution detection. To be specific, CR-Net integrates Structure-induced Hierarchical Feature Adaptation (SHFA) and Reliable Structural Adjacency Alignment (RSAA). SHFA module is introduced to establish structural correlations between targets and achieve structure-aware feature adaptation, thereby enhancing the interpretability of the feature adaptation process. Afterwards, the RSAA module is proposed to enhance reliable semantic alignment, by leveraging the secure adjacency set to transfer valuable discriminative knowledge from the source domain to the target domain. This further improves the discriminability of the detection model in the target domain. Based on experimental results from different-resolution datasets,the proposed CR-Net significantly enhances cross-resolution adaptation by preserving intra-domain structures and improving discriminability. It achieves state-of-the-art (SOTA) performance in cross-resolution SAR target detection.