Image super-resolution (SR) is widely used in remote sensing because it can effectively increase image details. Neural networks have shown remarkable performance in recent years, benefitting from their end-to-end training. However, remote sensing images contain a variety of degradation factors. Neural networks lack flexibility in dealing with these complex issues compared with reconstruction-based approaches. Traditional neural network methods can not take advantage of prior knowledge and lack interpretability. To develop a flexible, accurate, and interpretable algorithm for remote sensing SR, we proposed an effective SR network called YSRNet. It is performed by unfolding a traditional optimization process into a learnable network. Combining conventional reconstruction-based methods and neural networks can significantly improve the algorithm's performance. Since the gradient features of remote sensing images contain valuable information, the total variation (TV) constraints and the deep prior constraints are introduced into the objective function for image SR. Furthermore, we propose an enhanced version called YSRNet+, which can apply attention weights to different prior terms and channels. Compared with the YSRNet, the YSRNet+ enables networks to focus more on useful prior information and improve the interpretability of networks. Experiments on three remote sensing datasets are performed to evaluate the algorithm's effectiveness. The experimental results demonstrate that the proposed algorithm performs better than some state-of-the-art neural network algorithms, especially in the scenario of the multi-degradation factors.