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arXiv · 2405.16147

On Bobkov-Tanaka type spectrum for the double-phase operator

Laura Gambera·Umberto Guarnotta
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Abstract

Moving from the seminal papers by Bobkov and Tanaka \cite{BT,BT2,BT3} on the spectrum of the $(p,q)$-Laplacian, we analyze the case of the double-phase operator. We discuss the region of parameters in which existence and non-existence of positive solutions occur. The proofs are based on normalization procedures, the Nehari manifold, and truncation techniques, exploiting Picone-type inequalities and an ad-hoc strong maximum principle.

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Laura Gambera, Umberto Guarnotta. 2024-05-25. On Bobkov-Tanaka type spectrum for the double-phase operator. https://arxiv.org/abs/2405.16147

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