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Synthetic Aperture Radar (SAR) image recognition is vital for disaster monitoring, military reconnaissance, and ocean observation. However, large SAR image sizes hinder deep learning deployment on resource-constrained edge devices, and existing lightweight models struggle to balance high-precision feature extraction with low computational requirements. The emerging Kolmogorov-Arnold Network (KAN) enhances fitting by replacing fixed activations with learnable ones, reducing parameters and computation. Inspired by KAN, we propose Light-ResKAN to achieve a better balance between precision and efficiency. First, Light-ResKAN modifies ResNet by replacing convolutions with KAN convolutions, enabling adaptive feature extraction for SAR images. Second, we use Gram Polynomials as activations, which are well-suited for SAR data to capture complex non-linear relationships. Third, we employ a parameter-sharing strategy: each kernel shares parameters per channel, preserving unique features while reducing parameters and FLOPs. Our model achieves 99.09%, 93.01%, and 97.26% accuracy on MSTAR, FUSAR-Ship, and SAR-ACD datasets, respectively. Experiments on MSTAR resized to $1024 \times 1024$ show that compared to VGG16, our model reduces FLOPs by $82.90 \times$ and parameters by $163.78 \times$. This work establishes an efficient solution for edge SAR image recognition.