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Logarithmically Coupled \(p\)-Laplacian Systems: From Discrete Ground States to Rigidity and Critical Continuous Limits
This paper introduces a new coupled \(p\)-Laplacian system with logarithmic nonlinearities, on locally finite graphs and, in the critical case \(p=N>4\), on \(\mathbb R^N\) via a regularised formulation. The logarithmic coupling renders the energy functional ill-defined on the natural Sobolev space.
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