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.

An Ambrosetti–Prodi-type problem for the (p,q)-Laplacian operator

2019 ◽  
Vol 21 (01) ◽  
pp. 1750067
Author(s):  
Taísa Junges Miotto ◽  
Márcio Luís Miotto
Keyword(s):  
Existence Of Solutions ◽  
Laplacian Operator ◽  
Type Problem ◽  
Multiplicity Of Solutions ◽  
Existence And Multiplicity ◽  
Continuity Result

This work has objective to obtain results of existence and multiplicity of solutions for an Ambrosetti–Prodi-type problem for the [Formula: see text] operator. Moreover, it was proved a continuity result for the parameter which limits the existence of solutions in relation of the parameter [Formula: see text].

scholarly journals Existence and multiplicity of solutions for a fractional p-Laplacian equation with perturbation

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Zhen Zhi ◽  
Lijun Yan ◽  
Zuodong Yang
Keyword(s):  
Variational Methods ◽  
Bounded Domain ◽  
Analytical Techniques ◽  
Nontrivial Solutions ◽  
Multiplicity Results ◽  
Multiplicity Of Solutions ◽  
Laplacian Equation ◽  
Existence And Multiplicity

AbstractIn this paper, we consider the existence of nontrivial solutions for a fractional p-Laplacian equation in a bounded domain. Under different assumptions of nonlinearities, we give existence and multiplicity results respectively. Our approach is based on variational methods and some analytical techniques.

scholarly journals Solutions of Nonlocal -Laplacian Equations

2013 ◽  
Vol 2013 ◽  
pp. 1-7
Author(s):  
Mustafa Avci ◽  
Rabil Ayazoglu (Mashiyev)
Keyword(s):  
Laplace Operator ◽  
Variational Approach ◽  
Nonlocal Problem ◽  
Type Equation ◽  
Multiplicity Of Solutions ◽  
Kirchhoff Type ◽  
Existence And Multiplicity ◽  
Kirchhoff Type Equation ◽  
Laplacian Equations

In view of variational approach we discuss a nonlocal problem, that is, a Kirchhoff-type equation involving -Laplace operator. Establishing some suitable conditions, we prove the existence and multiplicity of solutions.

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.

scholarly journals Elliptic problems in variable exponent spaces

2006 ◽  
Vol 74 (2) ◽  
pp. 197-206 ◽  
Author(s):  
Mihai Mihailescu
Keyword(s):  
Variational Principle ◽  
Nonlinear Elliptic Equation ◽  
Variable Exponent ◽  
Mountain Pass Theorem ◽  
Growth Conditions ◽  
Cylindrical Symmetry ◽  
Multiplicity Results ◽  
Variable Exponent Spaces ◽  
Nonlinear Elliptic ◽  
Existence And Multiplicity

In this paper we study a nonlinear elliptic equation involving p(x)-growth conditions on a bounded domain having cylindrical symmetry. We establish existence and multiplicity results using as main tools the mountain pass theorem of Ambosetti and Rabinowitz and Ekeland's variational principle.

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.

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