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arXiv · 1911.06038

Extremal constant sign solutions and nodal solutions for the fractional p-Laplacian

Silvia Frassu·Antonio Iannizzotto
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Abstract

We study a pseudo-differential equation driven by the degenerate fractional p-Laplacian, under Dirichlet type conditions in a smooth domain. First we show that the solution set within the order interval given by a sub-supersolution pair is nonempty, directed, and compact, hence endowed with extremal elements. Then, we prove existence of a smallest positive, a biggest negative and a nodal solution, combining variational methods with truncation techniques.

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Silvia Frassu, Antonio Iannizzotto. 2019-11-14. Extremal constant sign solutions and nodal solutions for the fractional p-Laplacian. https://arxiv.org/abs/1911.06038

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