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Nonlinear anisotropic Picone type identities for general vector fields and applications

Acta Universitatis Sapientiae, Mathematica
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Picone’s identity on hyperbolic space and its applications

Bollettino dell'Unione Matematica Italiana, 2021
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Jagmohan Tyagi
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A TREATMENT OF STURM-LIOUVILLE EIGENVALUE PROBLEMS VIA PICONE'S IDENTITY

Analysis, 1985
In the present paper self-adjoint Sturm-Liouville eigenvalue problems of even order are considered. While the existing proofs of the classical results, in particular of Rayleigh's principle, use methods from the calculus of variations and from the theory of integral equations (in connection with Green's function), we derive these results from a ...
Kratz, W., Peyerimhoff, A.
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Generalized Picone Identity for the Finsler p-Laplacian and its Applications

Ukrainian Mathematical Journal, 2022
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Picone type identities and definiteness of quadratic functionals on time scales

Applied Mathematics and Computation, 2009
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Šimon Hilscher, Roman, Zeidan, Vera
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Picone identity for quasilinear elliptic equations with -Laplacians and Sturmian comparison theory

Applied Mathematics and Computation, 2013
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Caccioppoli estimates through an anisotropic Picone’s identity

Proceedings of the American Mathematical Society, 2014
Summary: Caccioppoli-type estimates for a class of nonlinear differential operators which include the \( p\)-Laplacian and the pseudo \( p\)-Laplacian as special cases are obtained by means of the differential identity involving an arbitrary norm in \( \mathbb{R}^n\) which generalizes the well-known multidimensional Picone's formula.
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Generalised nonlinear Picone identities for p-sub-Laplacians and p-biharmonic operators and applications

Advances in Operator Theory, 2021
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Durvudkhan Suragan, Nurgissa Yessirkegenov   +1 more
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New nonlinear Picone identities with variable exponents and applications

Commentationes Mathematicae Universitatis Carolinae
Summary: This paper introduces two novel nonlinear anisotropic Picone identities with variable exponents that expand upon the traditional identity used for the ordinary Laplace equation. Additionally, the research explores potential applications of these findings in anisotropic Sobolev spaces featuring variable exponents.
Khelifi, Hichem, El Hadfi, Youssef
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The application of Picone-type identity for some nonlinear elliptic differential equations

2003
Summary: There is established a Picone-type identity for the second order partial differential equation \[ \sum ^N_{i=1}\frac {\partial }{\partial x_i} \Biggl (r_i(x)\,\varphi \left (\frac {\partial u}{\partial x_i}\right)\Biggl) +\, c(x)\varphi (u) = 0, \quad \varphi (u) :=| u| ^{p-1}u,\;p>0.\leqno {(*)} \] Using this identity there is proved the ...
Bognár, G., Dosly, O.
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