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Article . 2024 . Peer-reviewed
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Article . 2024
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Article . 2024
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On a Neumann Problem with an Intrinsic Operator

Authors: Dumitru Motreanu; Angela Sciammetta;

On a Neumann Problem with an Intrinsic Operator

Abstract

This paper investigates the existence and location of solutions for a Neumann problem driven by a (p,q) Laplacian operator and with a reaction term that depends not only on the solution and its gradient but also incorporates an intrinsic operator, which is its main novelty. This paper can be seen as the study of a quasilinear Neumann problem involving an elaborated perturbation with a Nemytskij operator. The approach proceeds through a version of the sub/supersolution method, exploiting an invariance property regarding the sub/supersolution ordered interval with respect to the intrinsic operator. An example illustrates the applicability of our result.

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Keywords

intrinsic operator, positive solution, gradient dependence, neumann problem, sub/supersolution, QA1-939, Mathematics

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selected citations
These citations are derived from selected sources.
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
4
Top 10%
Average
Top 10%
gold
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