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arXiv · 2410.05185

Fractional p-Kirchhoff equation with Sobolev and Choquard singular nonlinearities

Ronaldo Brasileiro Assunção·Olímpio Hiroshi Miyagaki·Rafaella Ferreira dos Santos Siqueira
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Abstract

In the present work, we consider a fractional p-Kirchhoff equation in the entire space R^N featuring doubly nonlinearities, involving a generalized nonlocal Choquard subcritical term together with a local critical Sobolev term; the problem also includes a Hardy-type term; additionaly, all terms have critical singular weights. Our result improve upon previous work in the following ways: we focus our attention on the existence of a nontrivial weak solution for fractional p-Kirchhoff equation in the entire space R^N. The possibility of a slower growth in the nonlinearity makes it more difficult to establish a compactness condition; to do so, we use the Cerami condition. The crucial points in our argument are the uniform boundedness of the convolution part and the lack of compactness of the Sobolev embeddings.

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Ronaldo Brasileiro Assunção, Olímpio Hiroshi Miyagaki, Rafaella Ferreira dos Santos Siqueira. 2024-10-07. Fractional p-Kirchhoff equation with Sobolev and Choquard singular nonlinearities. https://arxiv.org/abs/2410.05185

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