Multiplicity results for a system involving the p(x)- Laplacian operator

2021 ◽  
pp. 1-10
Author(s):  
Leandro S. Tavares ◽  
J. Vanterler C. Sousa
Keyword(s):  
Laplacian Operator ◽  
Multiplicity Results

scholarly journals Existence and multiplicity results for a Steklov problem involving (p(x), q(x))-Laplacian operator

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Belhadj Karim ◽  
A. Lakhdi ◽  
M. R. Sidi Ammi ◽  
A. Zerouali
Keyword(s):  
Critical Points ◽  
Elliptic Problem ◽  
Laplacian Operator ◽  
Three Solutions ◽  
Multiplicity Results ◽  
Steklov Problem ◽  
Three Critical Points Theorem ◽  
Existence And Multiplicity

Abstract In this work, we are concerned with a generalized Steklov problem with (p(x), q(x))-Laplacian operator. Under some appropriate conditions on the data involved in the elliptic problem, we prove the existence of at least three solutions using Ricceri’s three critical points theorem.

scholarly journals On a nonlinear system arising in a theory of thermal explosion

2018 ◽  
Vol 38 (2) ◽  
pp. 167-172
Author(s):  
S. H. Rasouli
Keyword(s):  
Mathematical Model ◽  
Nonlinear System ◽  
Thermal Explosion ◽  
Positive Solutions ◽  
Laplacian Operator ◽  
Multiplicity Results ◽  
Bounded Smooth Domain ◽  
Existence And Multiplicity ◽  
Bounded Smooth ◽  
Multiplicity Of Positive Solutions

The purpose of this paper is to study the existence and multiplicity of positive solutions for a mathematical model of thermal explosion which is described by the system$$\left\{\begin{array}{ll}-\Delta u = \lambda f(v), & x\in \Omega,\\-\Delta v = \lambda g(u), & x\in \Omega,\\\mathbf{n}.\nabla u+ a(u) u=0 , & x\in\partial \Omega,\\\mathbf{n}.\nabla v+ b(v) v=0 , & x\in\partial \Omega,\\\end{array}\right.$$where $\Omega$ is a bounded smooth domain of $\mathbb{R}^{N},$ $\Delta$ is the Laplacian operator, $\lambda>0$ is a parameter, $f,g$ belong to a class of non-negative functions that have a combined sublinear effect at $\infty,$ and $a,b: [0,\infty) \rightarrow (0,\infty)$ are nondecreasing $C^{1}$ functions. We establish our existence and multiplicity results by the method of sub-- and supersolutions.

A variational approach to multiplicity results for boundary-value problems on the real line

2015 ◽  
Vol 145 (1) ◽  
pp. 13-29 ◽  
Author(s):  
Gabriele Bonanno ◽  
Giuseppina Barletta ◽  
Donal O’Regan
Keyword(s):  
Real Line ◽  
Nonlinear Term ◽  
Laplacian Operator ◽  
Multiplicity Result ◽  
Multiplicity Results ◽  
The Real ◽  
Existence And Multiplicity ◽  
Superlinear Growth ◽  
Unbounded Intervals ◽  
Special Case

We study the existence and multiplicity of solutions for a parametric equation driven by the p-Laplacian operator on unbounded intervals. Precisely, by using a recent local minimum theorem we prove the existence of a non-trivial non-negative solution to an equation on the real line, without assuming any asymptotic condition either at 0 or at ∞ on the nonlinear term. As a special case, we note the existence of a non-trivial solution for the problem when the nonlinear term is sublinear at 0. Moreover, under a suitable superlinear growth at ∞ on the nonlinearity we prove a multiplicity result for such a problem.

scholarly journals Existence and multiplicity results for quasilinear elliptic equations

2005 ◽  
Vol 71 (3) ◽  
pp. 377-386 ◽  
Author(s):  
Wei Dong
Keyword(s):  
Positive Solutions ◽  
Elliptic Equations ◽  
Quasilinear Elliptic Equations ◽  
Laplacian Operator ◽  
Multiplicity Results ◽  
Existence And Multiplicity ◽  
Bounded Open Subset ◽  
Multiplicity Of Positive Solutions ◽  
Quasilinear Elliptic ◽  
Laplacian Operators

The goal of this paper is to study the multiplicity of positive solutions of a class of quasilinear elliptic equations. Based on the mountain pass theorems and sub-and supersolutions argument for p-Laplacian operators, under suitable conditions on nonlinearity f(x, s), we show the follwing problem: , where Ω is a bounded open subset of RN, N ≥ 2, with smooth boundary, λ is a positive parameter and ∆p is the p-Laplacian operator with p > 1, possesses at least two positive solutions for large λ.

PERIODIC SOLUTIONS FOR SINGULAR PERTURBATIONS OF THE SINGULAR ϕ-LAPLACIAN OPERATOR

2013 ◽  
Vol 15 (04) ◽  
pp. 1250063 ◽  
Author(s):  
CRISTIAN BEREANU ◽  
DANA GHEORGHE ◽  
MANUEL ZAMORA
Keyword(s):  
Periodic Solutions ◽  
Nonlinear Elasticity ◽  
Singular Perturbations ◽  
Continuous Functions ◽  
Lower And Upper Solutions ◽  
Laplacian Operator ◽  
Multiplicity Results ◽  
Existence And Multiplicity ◽  
Periodic Problems ◽  
Singular Nonlinearities

In this paper, using Leray–Schauder degree arguments and the method of lower and upper solutions, we give existence and multiplicity results for periodic problems with singular nonlinearities of the type [Formula: see text] where r, n, e : [0, T] → ℝ are continuous functions and λ > 0. We also consider some singular nonlinearities arising in nonlinear elasticity or of Rayleigh–Plesset type.

scholarly journals On a Robin type problem involving 𝑝(𝑥)-Laplacian operator

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Abdesslem Ayoujil ◽  
Anass Ourraoui
Keyword(s):  
Variational Approach ◽  
Growth Conditions ◽  
Laplacian Operator ◽  
Robin Problem ◽  
Type Problem ◽  
Multiplicity Results ◽  
Multiplicity Of Solutions ◽  
Existence And Multiplicity ◽  
Cerami Condition ◽  
Weaker Conditions

Abstract This paper deals with the existence and multiplicity of solutions for the p ⁢ ( x ) p(x) -Laplacian Robin problem without the well-known Ambrosetti–Rabinowitz type growth conditions. By means of the variational approach (with the Cerami condition), existence and multiplicity results of solutions are established under weaker conditions.

Multiplicity of Solutions to Elliptic Problems Involving the 1-Laplacian with a Critical Gradient Term

2017 ◽  
Vol 17 (2) ◽  
Author(s):  
Boumediene Abdellaoui ◽  
Andrea Dall’Aglio ◽  
Sergio Segura de León
Keyword(s):  
Dirichlet Problem ◽  
Radon Measure ◽  
Laplacian Operator ◽  
Gradient Term ◽  
Multiplicity Result ◽  
Unbounded Solution ◽  
Multiplicity Results ◽  
Positive Radon Measure ◽  
Disjoint Sets ◽  
Strong Multiplicity

AbstractIn the present paper we study the Dirichlet problem for an equation involving the 1-Laplacian and a total variation term as reaction. We prove a strong multiplicity result. Namely, we show that for any positive Radon measure concentrated in a set away from the boundary and singular with respect to a certain capacity, there exists an unbounded solution, and measures supported on disjoint sets generate different solutions. These results can be viewed as the analogue for the 1-Laplacian operator of some known multiplicity results which were first obtained by Ireneo Peral, to whom this article is dedicated, and his collaborators.

scholarly journals Positive Solutions of Fractional Differential Equations with p-Laplacian

2017 ◽  
Vol 2017 ◽  
pp. 1-9 ◽  
Author(s):  
Yuansheng Tian ◽  
Sujing Sun ◽  
Zhanbing Bai
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Differential Equations ◽  
Positive Solution ◽  
Fractional Differential Equations ◽  
Laplacian Operator ◽  
Point Boundary ◽  
Multiplicity Results ◽  
New Class ◽  
Fractional Differential

The multiplicity of positive solution for a new class of four-point boundary value problem of fractional differential equations with p-Laplacian operator is investigated. By the use of the Leggett-Williams fixed-point theorem, the multiplicity results of positive solution are obtained. An example is given to illustrate the main results.

scholarly journals Multiplicity Results forp-Laplacian with Critical Nonlinearity of Concave-Convex Type and Sign-Changing Weight Functions

2009 ◽  
Vol 2009 ◽  
pp. 1-24 ◽  
Author(s):  
Tsing-San Hsu
Keyword(s):  
Continuous Functions ◽  
Nehari Manifold ◽  
Weight Functions ◽  
Laplacian Operator ◽  
Positive Real ◽  
Multiplicity Results ◽  
Bounded Smooth ◽  
Positive Real Parameter ◽  
The Nehari Manifold ◽  
Quasilinear Elliptic

The multiple results of positive solutions for the following quasilinear elliptic equation: in on , are established. Here, is a bounded smooth domain in denotes the -Laplacian operator, is a positive real parameter, and are continuous functions on which are somewhere positive but which may change sign on . The study is based on the extraction of Palais-Smale sequences in the Nehari manifold.

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