3 problems
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The conjecture that uniqueness requires admitting only smooth solutions
Smooth-solution uniqueness conjecture. To achieve uniqueness, only smooth solutions should be admitted.
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The MPEP and expected exit-time conjecture for periodically driven nonlinear oscillators
MPEP and expected exit-time conjecture. Similar large-deviation results for the most probable escape paths and the expected exit times hold for oscillators of the form $$ .
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Non-resonance conjecture for breather continuation with decaying potentials
Non-resonance conjecture. In this setting, the non-resonance condition should be replaced by