Autonomous agents can adapt their behaviour to changing environments, but remain bound to requirements, goals, and capabilities fixed at design time, preventing genuine software evolution. This paper introduces self-evolving software agents, combining BDI reasoning with LLMs to enable autonomous evolution of goals, reasoning, and executable code. We propose a BDI-LLM architecture in which an automated evolution module operates alongside the agent's reasoning loop, eliciting new requirements from experience and synthesizing corresponding design and code updates. A prototype evaluated in a dynamic multi-agent environment shows that agents can autonomously discover new goals and generate executable behaviours from minimal prior knowledge. The results indicate both the feasibility and current limits of LLM-driven evolution, particularly in terms of behavioural inheritance and stability.