Existence result for some elliptic quasilinear equation involving the N-Laplacian in $$ \mathbb {R}^N $$RN with a large class of nonlinearities

2018 ◽  
Vol 67 (2) ◽  
pp. 875-889 ◽  
Author(s):  
Sami Aouaoui
Keyword(s):  
Large Class ◽  
Existence Result ◽  
Quasilinear Equation ◽  
Elliptic Quasilinear Equation

scholarly journals Liouville Results and Asymptotics of Solutions of a Quasilinear Elliptic Equation with Supercritical Source Gradient Term

2020 ◽  
Vol 21 (1) ◽  
pp. 57-76
Author(s):  
Marie-Françoise Bidaut-Véron
Keyword(s):  
Quasilinear Equation ◽  
Continuous Functions ◽  
Finite Limit ◽  
Gradient Term ◽  
Type Estimate ◽  
Liouville Type ◽  
Asymptotics Of Solutions ◽  
Type Property ◽  
Elliptic Quasilinear Equation ◽  
Quasilinear Elliptic

Abstract We consider the elliptic quasilinear equation - Δ m ⁢ u = u p ⁢ | ∇ ⁡ u | q {-\Delta_{m}u=u^{p}\lvert\nabla u\rvert^{q}} in ℝ N {\mathbb{R}^{N}} , q ≥ m {q\geq m} and p > 0 {p>0} , 1 < m < N {1<m<N} . Our main result is a Liouville-type property, namely, all the positive C 1 {C^{1}} solutions in ℝ N {\mathbb{R}^{N}} are constant. We also give their asymptotic behaviour; all the solutions in an exterior domain ℝ N ∖ B r 0 {\mathbb{R}^{N}\setminus B_{r_{0}}} are bounded. The solutions in B r 0 ∖ { 0 } {B_{r_{0}}\setminus\{0\}} can be extended as continuous functions in B r 0 {B_{r_{0}}} . The solutions in ℝ N ∖ { 0 } {\mathbb{R}^{N}\setminus\{0\}} has a finite limit l ≥ 0 {l\geq 0} as | x | → ∞ {\lvert x\rvert\to\infty} . Our main argument is a Bernstein estimate of the gradient of a power of the solution, combined with a precise Osserman-type estimate for the equation satisfied by the gradient.

scholarly journals Remarks on quasilinear evolutions equations

1991 ◽  
Vol 14 (4) ◽  
pp. 731-736
Author(s):  
James E. Munoz Rivera
Keyword(s):  
Initial Data ◽  
Boundary Conditions ◽  
Existence Result ◽  
Quasilinear Equation ◽  
Classical Solutions

In this paper we study the existence result of classical solutions for the quasilinear equationutt−Δu−M(∫Ω|∇u|2dx)Δutt=f, with initial datau(0)=u0,u(1)=u1and homogeneous boundary conditions.

A quasilinear problem without the Ambrosetti–Rabinowitz-type condition

2010 ◽  
Vol 140 (2) ◽  
pp. 391-398 ◽  
Author(s):  
Leonelo Iturriaga ◽  
Sebastián Lorca ◽  
Pedro Ubilla
Keyword(s):  
Positive Solution ◽  
Existence Result ◽  
Quasilinear Equation ◽  
Laplacian Operator ◽  
Main Difficulty ◽  
Type Condition ◽  
Change Of Variables ◽  
Quasilinear Problem

We study the existence of a positive solution of a p-superlinear equation involving the p-Laplacian operator. The main difficulty here is that the nonlinearity considered does not necessarily verify the well-known Ambrosetti–Rabinowitz condition. As an application, by performing an adequate change of variables we obtain an existence result of a quasilinear equation depending on the gradient.

A Large Class of p-Ary Cyclic Codes and Sequence Families

2010 ◽  
Vol E93-A (11) ◽  
pp. 2272-2277
Author(s):  
Zhengchun ZHOU ◽  
Xiaohu TANG ◽  
Udaya PARAMPALLI
Keyword(s):  
Large Class ◽  
Cyclic Codes

The Social Furniture of Virtual Worlds

Disputatio ◽  
2019 ◽  
Vol 11 (55) ◽  
pp. 345-369
Author(s):  
Peter Ludlow
Keyword(s):  
Large Class ◽  
Data Structures ◽  
Virtual Worlds ◽  
Causal Powers ◽  
Virtual Objects ◽  
David Chalmers ◽  
The Social

AbstractDavid Chalmers argues that virtual objects exist in the form of data structures that have causal powers. I argue that there is a large class of virtual objects that are social objects and that do not depend upon data structures for their existence. I also argue that data structures are themselves fundamentally social objects. Thus, virtual objects are fundamentally social objects.

Computing Cores for Existential Rules with the Standard Chase and ASP

2020 ◽  
Author(s):  
Markus Krötzsch
Keyword(s):  
Large Class ◽  
Data Exchange ◽  
Answer Set Programming ◽  
Query Answering ◽  
Universal Model ◽  
The Core ◽  
Universal Models ◽  
General Terms ◽  
Special Cases ◽  
The Many

To reason with existential rules (a.k.a. tuple-generating dependencies), one often computes universal models. Among the many such models of different structure and cardinality, the core is arguably the “best”. Especially for finitely satisfiable theories, where the core is the unique smallest universal model, it has advantages in query answering, non-monotonic reasoning, and data exchange. Unfortunately, computing cores is difficult and not supported by most reasoners. We therefore propose ways of computing cores using practically implemented methods from rule reasoning and answer set programming. Our focus is on cases where the standard chase algorithm produces a core. We characterise this desirable situation in general terms that apply to a large class of cores, derive concrete approaches for decidable special cases, and generalise these approaches to non-monotonic extensions of existential rules.

Modifikasi Sistem Asistensi dan Responsi Kelas Kecil pada Praktikum Parasitologi Blok Digestif dan Hematoimunologi Fakultas Kedokteran Universitas Riau

2017 ◽  
Vol 8 (1) ◽  
pp. 46
Author(s):  
Suri Dwi Lesmana ◽  
Esy Maryanti
Keyword(s):  
Large Class ◽  
Teaching And Learning ◽  
Learning Activities ◽  
Small Class ◽  
Laboratory Practice ◽  
Large Classes ◽  
Average Value ◽  
Competency Based

Faculty of Medicine University of Riau has been implementing Competency Based Curriculum (KBK) with theProblem Based Learning (PBL) since 2007 with the implementation of teaching and learning activities of the systemconsists of a tutorial activities, skillab, expert lectures, independent and practical. However, there are still manyproblems in the implementation of the KBK on preclinic degree. One part of the block that is identified to be one ofthe causes of low graduation exam block is less efective coaching laboratory practice. Parasitology is one part of thetask is to provide laboratory practice in several blocks on the stage of preclinic especially digestive and hematoimunologyblock. This study aimed to compare the results of the evaluation of parasitology laboratory practice in hematoimunologyand digestive assistance and posttest in large classes with small class. Assistance and posttest in large class performedon the digestive block implementation and hematoimunologi in 2011 while assisting and posttest of small classes ona block implementation in 2012. Average value of small class digestive laboratory practice was not significantlylower than the large class but the proportion of the value of quality B and C more many in small classes. The meanvalue of the block hematoimunologi laboratory practice significantly higher on small class assistance and posttest aswell as the proportion of the value of quality A, B and C was higher in small classes than large classes.

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