Normalized solutions to elliptic problems - new minimization technique

We propose a simple minimization technique to demonstrate the existence of least-energy solutions for certain nonlinear elliptic equations with a prescribed L2-norm. Our approach relies on the direct minimization of a variational functional, restricted to the intersection of the linear combination of Nehari and Pohozaev constraints with the closed L2-ball. This method allows us to address most of the known physical examples of nonlinearities discussed in the literature.