A strong maximum principle for differential equations with nonstandard <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si1.gif" overflow="scroll"><mml:mi>p</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:mi>x</mml:mi><mml:mo stretchy="false">)</mml:mo></mml:math>-growth conditions

This paper deals with the existence of positively solution and its asymptotic behavior for parabolic system of ( p ( x ) , q ( x ) ) -Laplacian system of partial differential equations using a sub and super solution according to some given boundary conditions, Our result is an extension of Boulaaras’s works which studied the stationary case, this idea is new for evolutionary case of this kind of problem.

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“…is increasing function.It is easy to verify that A is a continuous bounded mapping. By the proof ( [12]).…”

Section: We Considere Mappingmentioning

confidence: 75%

Existence of Positive Solutions and Its Asymptotic Behavior of (p(x), q(x))-Laplacian Parabolic System

et al. 2019

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“…Strong maximum principle for anisotropic singular double phase problems. The main result of this subsection here extends Theorem 1.1 of Zhang [59], which does not cover the case of the anisotropic (p, q)-Laplacian see conditions ( 5), ( 6) in [59] . A maximum principle for isotropic double phase problems was proved recently by Papageorgiou, Vetro and Vetro [47].…”

Section: 1mentioning

confidence: 78%

Anisotropic singular double phase Dirichlet problems

Papageorgiou¹,

Rădulescu²,

Zhang³

2021

DCDS-S

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<p style='text-indent:20px;'>We consider an anisotropic double phase problem with a reaction in which we have the competing effects of a parametric singular term and a superlinear perturbation. We prove a bifurcation-type result describing the changes in the set of positive solutions as the parameter varies on <inline-formula><tex-math id="M1">\begin{document}$ \mathring{\mathbb{R}}_+ = (0, +\infty) $\end{document}</tex-math></inline-formula>. Our approach uses variational tools together with truncation and comparison techniques as well as several general results of independent interest about anisotropic equations, which are proved in the Appendix.</p>

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“…Then from Tan-Fang [24, Corollary 3.1] (see also Fukagai-Narukawa [6, Lemma 3.3]), we have that u 0 ∈ C + \ {0}. Finally, the anisotropic maximum principle of Zhang [25] implies that u 0 ∈ int C + . Now let λ ∈ (0, λ + ) and consider 0 < γ < λ.…”

Section: Note Thatmentioning

confidence: 89%

Constant sign and nodal solutions for parametric anisotropic (p, 2) -equations

Papageorgiou

Repovš

Vetro

2021

Applicable Analysis

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A strong maximum principle for differential equations with nonstandard p(x)-growth conditions

Abstract: In this paper, with some special technics, we give a strong maximum principle for the equations with nonstandard p(x)-growth conditionswhere ϕ(x, s), d(x), f (x, u) satisfy some conditions.  2005 Elsevier Inc. All rights reserved.

Cited by 113 publications

References 24 publications

Existence of Positive Solutions and Its Asymptotic Behavior of (p(x), q(x))-Laplacian Parabolic System

Existence of Positive Solutions and Its Asymptotic Behavior of (p(x), q(x))-Laplacian Parabolic System

Anisotropic singular double phase Dirichlet problems

Constant sign and nodal solutions for parametric anisotropic (p, 2) -equations

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