| Abstract: |
| Normalized solutions for elliptic PDEs are sought under a prescribed mass constraint and appear naturally in models from nonlinear physics. In this talk, we will discuss recent results for normalized solutions to nonlinear elliptic problems involving Kirchhoff, Choquard, fractional, and weighted Caffarelli-Kohn-Nirenberg type operators. The focus will be on variational methods under mass constraint, where critical growth, nonlocal effects, and loss of compactness create significant difficulties. Using Pohozaev-type identities, fibering maps, and minimax arguments, one can establish existence, multiplicity, and ground state solutions in several regimes. These results demonstrate that constrained variational techniques provide a unified framework for studying normalized solutions in modern elliptic PDEs. |
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