The rapid growth of biomedical literature presents a major challenge for organizing knowledge and identifying emerging research trends. While PubMed provides effective access to relevant articles, it does not support understanding the conceptual structure of document collections. Existing tools rely on predefined features, ontologies, or parameter-sensitive clustering methods, limiting their ability to uncover fine-grained, data-driven topics in a reproducible manner. We present BioTopicXplor, an on-demand web server for interactive exploration of biomedical literature derived from arbitrary PubMed queries. The system integrates ConvexTopics, a convex optimization?based topic modeling framework that guarantees convergence to a global optimum and eliminates the need for predefined parameters. This enables the generation of reproducible and fine-grained topic structures across large document collections. Given a PubMed query, BioTopicXplor retrieves relevant articles, performs topic discovery, and organizes the resulting subtopics into a hierarchical structure of higher-level themes. To enhance interpretability, the system incorporates large language models to generate concise, literature-grounded summaries and descriptive titles for each topic, with links to supporting evidence. We demonstrate the utility of BioTopicXplor through a case study on anti-aging research, where the system reveals meaningful thematic structures and supports knowledge discovery.