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

2024/05/25 by Gambera, Laura, Guarnotta, Umberto
#35B38 #35J25 #35J60 #35P30 #Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2405.16147

Abstract

Moving from the seminal papers by Bobkov and Tanaka \citeBT,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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