Normalized solutions for magnetic p-Laplacian equations coupled with nonlocal Poisson potentials and critical nonlinearities

We investigate the existence and multiplicity of normalized solutions to the magnetic Schrödinger-Poisson system with critical Sobolev exponent and a p-Laplacian operator:under the mass constraint where is a Lagrange multiplier, and is the critical Sobolev exponent. The operator denotes the magnetic p-Laplacian, incorporating a vector potential which introduces new challenges due to the lack of gauge invariance and anisotropic effects. For the Lp-subcritical case we employ the truncation method, concentration-compactness principles, and genus theory to prove the existence of infinitely many solutions. In the Lp-supercritical regime we use a modified Pohozaev manifold and mountain pass arguments to establish the existence of at least one normalized solution. The critical role of the magnetic potential A is analyzed, showing how it influences the compactness properties and energy levels of the system. This work provides the first results on normalized solutions for the p-Laplacian Schrödinger-Poisson system with magnetic fields and critical nonlinearities, extending previous studies in both the non-magnetic case and the semilinear setting p = 2. Our results have potential implications for models in quantum physics where magnetic interactions and mass preservation are fundamental.