Results 11 to 20 of about 391 (135)
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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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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A new variable exponent Picone identity and applictions [PDF]
Mathematical Inequalities & Applications, 2019 Summary: In this paper, we derive a new variable exponent Picone identity for \(p(x)\)-Laplacian, which contains some known Picone identities. As applications, a strict monotonicity of principal eigenvalues with respect to domains for the eigenvalue problems to \(p(x)\)-Laplace equation, a variable exponent Barta type inequality, a variable exponent ...
Feng, Tingfu, Han, Junqiang
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A Picone's identity for the p(x)-Laplace equations and its applications [PDF]
Mathematical Inequalities & Applications, 2021 Summary: In this paper, we present a Picone identity for the \(p(x)\)-Laplace equations and establish some applications of this formula, such as Caccioppoli inequalities, nonexistence of positive supersolutions, domain monotonicity property, uniqueness and simplicity of the first eigenvalue, Hardy type inequality, Barta-type inequality, a nonlinear ...
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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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The Picone identity for a class of partial differential equations [PDF]
Mathematica Bohemica, 2002 Summary: The Picone-type identity for the half-linear second order partial differential equation \[ \sum _{i=1}^n\frac {\partial }{\partial x_i} \Phi \bigg (\frac {\partial u}{\partial x_i}\bigg )+c(x)\Phi (u)=0,\quad \Phi (u):=| u| ^{p-2}u,\;p>1, \] is established and some applications of this identity are suggested.
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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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Electronic Journal of Differential Equations, 2021 In this article, we study a class of doubly nonlinear parabolic problems involving the fractional p-Laplace operator. For this problem, we discuss existence, uniqueness and regularity of the weak solutions by using the time-discretization method and ...
Jacques Giacomoni +2 more
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