Recent content by mblasco137

Thank you for the suggestions and the encouragement! Calculus of variations and Morse theory are certainly relevant to understanding the critical-point structure of energy functionals. I’m particularly interested in how these methods connect with spectral analysis and rigorous nonlinear...

A standard example is a gyroscopically stabilized system, such as a spinning top (dreidel). Its upright configuration can be dynamically stable under suitable conditions even though it’s not a local minimum of the gravitational potential energy. The important distinction is that dynamical...

In principle, yes. If the Hessian of the energy functional has a negative direction then that identifies a saddle point rather than a local minimum. However, for nonlinear field theories with infinitely many degrees of freedom, constraints, and continuous spectra, establishing the relevant...

That’s a sufficient criterion under appropriate assumptions but I would distinguish energy minimization from a universal stability criterion. A strict local minimum of an appropriately conserved energy functional can establish Lyapunov stability under suitable conditions but the converse does...

It answers only a small part of the original question by establishing that stationarity alone is insufficient to demonstrate stability. However, my broader question concerns which additional mathematical conditions are necessary to establish spectral, orbital, or nonlinear stability, and how...

Thank you for the clarification. My research has not yet been published in a peer-reviewed journal and I understand the forum’s restrictions regarding unpublished theories. My intention was not to introduce or promote a personal framework, but to discuss the established mathematical distinction...

Yes, there are several well-established examples in nonlinear field theory where stationary solutions exist mathematically but are dynamically unstable. A classic example is the sphaleron in electroweak theory. It is a static, finite-energy solution of the field equations but it possesses an...

In nonlinear classical field theories that admit localized or topological solutions (for example, Skyrme-type or Faddeev–Skyrme-type models), what mathematical and numerical evidence is normally considered sufficient to distinguish a genuinely stable localized solution from a stationary...