The existence and nonexistence for time nonlocal evolution equations with superlinear sources

Xi Huang; Li Peng

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arXiv · 2607.13177

The existence and nonexistence for time nonlocal evolution equations with superlinear sources

Xi Huang·Li Peng

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Abstract

We consider the solvable behaviour for the initial value problem of time nonlocal evolution equations with the kernels of type $(\mathcal{PC})$. Our aim is to analyze some sufficient conditions ensuring local existence, integrability of mild solutions when the nonlinear term exhibits rapid growth. Moreover, a sufficient condition of the unsolvable result is also established. It turns out that the solvable behaviour is closely connected with the index on the initial value, which occurs a critical dimension phenomenon. The proofs rely on subordination and monotone iterative method. Finally, several examples are given to illustrate the wide applicability of the results.

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Xi Huang, Li Peng. 2026-07-14. The existence and nonexistence for time nonlocal evolution equations with superlinear sources. https://arxiv.org/abs/2607.13177

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