Title:	Generalized Picone inequalities and their applications to (p,q)-Laplace equations
Authors:	Bobkov, Vladimír Tanaka, Mieko
Citation:	BOBKOV, V., TANAKA, M. Generalized Picone inequalities and their applications to (p,q)-Laplace equations. Open Mathematics, 2020, roč. 18, č. SEP 30 2020, s. 1030-1044. ISSN 2391-5455.
Issue Date:	2020
Publisher:	De Gruyter
Document type:	článek article
URI:	2-s2.0-85093669675 http://hdl.handle.net/11025/42767
ISSN:	2391-5455
Keywords in different language:	Picone inequality;Picone identity;(p,q)-Laplacian;nonexistence;positive solutions
Abstract in different language:	We obtain a generalization of the Picone inequality which, in combination with the classical Picone inequality, appears to be useful for problems with the (p,q)-Laplace type operators. With its help, as well as with the help of several other known generalized Picone inequalities, we provide some nontrivial facts on the existence and nonexistence of positive solutions to the zero Dirichlet problem for the equation −Δ𝑝𝑢 − Δ𝑞𝑢 = 𝑓𝜇(𝑥, 𝑢,∇𝑢) in a bounded domain Ω ⊂ R𝑁 under certain assumptions on the nonlinearity and with a special attention to the resonance case 𝑓𝜇(𝑥, 𝑢,∇𝑢) = 𝜆1(𝑝)|𝑢|𝑝−2𝑢 + 𝜇|𝑢|𝑞−2𝑢, where 𝜆1(𝑝) is the first eigenvalue of the p-Laplacian.
Rights:	© De Gruyter
Appears in Collections:	Články / Articles (NTIS) OBD

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