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On the existence of a nodal solution for p-Laplacian equations depending on the gradient

Part of: Elliptic equations and systems

Published online by Cambridge University Press:  31 January 2024

F. Faraci  and
D. Puglisi
F. Faraci
Affiliation:
Department of Mathematics and Computer Sciences, University of Catania, 95125 Catania, Italy (ffaraci@dmi.unict.it, dpuglisi@dmi.unict.it)
D. Puglisi
Affiliation:
Department of Mathematics and Computer Sciences, University of Catania, 95125 Catania, Italy (ffaraci@dmi.unict.it, dpuglisi@dmi.unict.it)
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Abstract

In the present paper we deal with a quasi-linear elliptic equation depending on a sublinear nonlinearity involving the gradient. We prove the existence of a nontrivial nodal solution employing the theory of invariant sets of descending flow together with sub-supersolution techniques, gradient regularity arguments, strong comparison principle for the $p$-Laplace operator. The same conclusion is obtained for an eigenvalue problem under a different set of assumptions.

Keywords

p-Laplace operatorgradient dependencenodal solutiongradient flow

MSC classification

Primary: 35J60: Nonlinear elliptic equations
Secondary: 35J92: Quasilinear elliptic equations with $p$-Laplacian
Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , First View , pp. 1 - 22
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Copyright
Copyright © The Author(s), 2024. Published by Cambridge University Press on behalf of The Royal Society of Edinburgh

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