Results 1 to 10 of about 336 (90)
A Picone identity for variable exponent operators and applications
Advances in Nonlinear Analysis, 2019 In this work, we establish a new Picone identity for anisotropic quasilinear operators, such as the p(x)-Laplacian defined as div(|∇ u|p(x)−2 ∇ u).
Arora Rakesh +2 more
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Generalized Picone inequalities and their applications to (p,q)-Laplace equations
Open Mathematics, 2020 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)(p,q)-Laplace-type operators.
Bobkov Vladimir, Tanaka Mieko
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Sturm-Picone Comparison Theorem of Second-Order Linear Equations on Time Scales
Advances in Difference Equations, 2009 This paper studies Sturm-Picone comparison theorem of second-order linear equations on time scales. We first establish Picone identity on time scales and obtain our main result by using it.
Zhang Chao, Sun Shurong
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Picone-type identity and comparison results for a class of partial differential equations of order 4m [PDF]
Opuscula Mathematica, 2013 In the paper, a Picone-type identity for the weighted \(p\)-polyharmonic operator is established and comparison theorems and other qualitative results for a class of half-linear partial differential equations of the \(4m\)th order based on this identity ...
Jaroslav Jaroš
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Anisotropic Picone identities and anisotropic Hardy inequalities
Journal of Inequalities and Applications, 2017 In this paper, we derive an anisotropic Picone identity for the anisotropic Laplacian, which contains some known Picone identities. As applications, a Sturmian comparison principle to the anisotropic elliptic equation and an anisotropic Hardy type ...
Tingfu Feng, Xuewei Cui
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Advances in Difference Equations, 2020 We show the global structure of the set of positive solutions of a discrete Dirichlet problem involving the p-Laplacian difference operator suggesting suitable conditions on the weight function and nonlinearity.
Liping Wei, Ruyun Ma
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Caccioppoli-type inequalities for Dirac operators
Journal of Inequalities and Applications, 2022 In this paper, we establish the Caccioppoli estimates for the nonlinear differential equation − D ‾ ( | D v | p − 2 D v ) = λ | v | p − 2 v , 1 < p < ∞ , $$ - \overline{D}\bigl( \vert Dv \vert ^{p-2}Dv\bigr) = \lambda \vert v \vert ^{p-2}v, \quad 1< p ...
Ardak Kashkynbayev, Gulaiym Oralsyn
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Advanced Nonlinear Studies, 2023 In this article, we study the uniqueness of positive symmetric solutions of the following mean curvature problem in Euclidean space: (P)u′1+∣u′∣2′+h(x)f(u)=0 ...
Lee Yong-Hoon, Yang Rui
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A generalized nonlinear Picone identity for the p-biharmonic operator and its applications
Journal of Inequalities and Applications, 2019 A generalized nonlinear Picone identity for the p-biharmonic operator is established in this paper. As applications, a Sturmian comparison principle to the p-biharmonic equation with singular term, a Liouville’s theorem to the p-biharmonic system, and a ...
Tingfu Feng
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Electronic Journal of Qualitative Theory of Differential Equations, 2018 We consider a nonlinear elliptic problem driven by the Dirichlet $p$-Laplacian and a reaction term which depends also on the gradient (convection). No growth condition is imposed on the reaction term $f(z, \cdot,y)$.
Nikolaos Papageorgiou +2 more
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