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 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.

Existence and multiplicity of periodic solutions to differential equations with attractive singularities

2021 ◽  
pp. 1-26
Author(s):  
José Godoy ◽  
Robert Hakl ◽  
Xingchen Yu
Keyword(s):  
Differential Equations ◽  
Periodic Solutions ◽  
Topological Degree ◽  
A Priori ◽  
New Method ◽  
Multiplicity Results ◽  
Existence And Multiplicity ◽  
Upper And Lower Functions

The existence and multiplicity of T-periodic solutions to a class of differential equations with attractive singularities at the origin are investigated in the paper. The approach is based on a new method of construction of strict upper and lower functions. The multiplicity results of Ambrosetti–Prodi type are established using a priori estimates and certain properties of topological degree.

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.

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