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math.AP2025
Simplicity and boundary behavior of spike sequences for a superlinear problem in plasma physics
Paolo Cosentino, Francesco Malizia
We prove that spike sequences related to a nonlinear problem of Grad-Shafranov type are always simple and always converge toward interior points of the domain. This sharpens the bl…
math.AP2024
Compactness of Palais-Smale sequences with controlled Morse Index for a Liouville type functional
Francesco Malizia
We prove that Palais-Smale sequences for Liouville type functionals on closed surfaces are precompact whenever they satisfy a bound on their Morse index. As a byproduct, we obtain…