scholarly journals An integro-differential inequality related to the smallest positive eigenvalue of p(x)-Laplacian Dirichlet problem

2016 ◽  
Vol 15 (1) ◽  
pp. 27-36
Author(s):  
Damian Wiśniewski ◽  
Mariusz Bodzioch
Keyword(s):  
Dirichlet Problem ◽  
Eigenvalue Problem ◽  
Unit Sphere ◽  
Differential Inequality ◽  
Beltrami Operator ◽  
Positive Eigenvalue ◽  
Differential Inequalities

AbstractWe consider the eigenvalue problem for the p(x)-Laplace-Beltrami operator on the unit sphere. We prove same integro-differential inequalities related to the smallest positive eigenvalue of this problem.

Existence of the first eigenvalue of the eigenvalue problem for the Laplace-Beltrami operator on the unit sphere

2018 ◽  
Vol 55 (3) ◽  
pp. 374-382
Author(s):  
Mariusz Bodzioch ◽  
Mikhail Borsuk ◽  
Sebastian Jankowski
Keyword(s):  
Eigenvalue Problem ◽  
Asymptotic Behaviour ◽  
Unit Sphere ◽  
Beltrami Operator ◽  
Positive Eigenvalue ◽  
Conical Point ◽  
First Eigenvalue ◽  
The First Eigenvalue ◽  
Asymptotic Behaviour Of Solutions ◽  
Oblique Derivative Problems

In this paper we formulate and prove that there exists the first positive eigenvalue of the eigenvalue problem with oblique derivative for the Laplace-Beltrami operator on the unit sphere. The firrst eigenvalue plays a major role in studying the asymptotic behaviour of solutions of oblique derivative problems in cone-like domains. Our work is motivated by the fact that the precise solutions decreasing rate near the boundary conical point is dependent on the first eigenvalue.

scholarly journals A singular eigenvalue problem for the Dirichlet (p, q)-Laplacian

2021 ◽  
Author(s):  
Yunru Bai ◽  
Nikolaos S. Papageorgiou ◽  
Shengda Zeng
Keyword(s):  
Dirichlet Problem ◽  
Eigenvalue Problem ◽  
Positive Solution ◽  
Positive Solutions ◽  
Singular Term ◽  
Type Theorem ◽  
Solution Map ◽  
Continuity Properties ◽  
Variational Tools ◽  
Superlinear Reaction

AbstractWe consider a parametric nonlinear, nonhomogeneous Dirichlet problem driven by the (p, q)-Laplacian with a reaction involving a singular term plus a superlinear reaction which does not satisfy the Ambrosetti–Rabinowitz condition. The main goal of the paper is to look for positive solutions and our approach is based on the use of variational tools combined with suitable truncations and comparison techniques. We prove a bifurcation-type theorem describing in a precise way the dependence of the set of positive solutions on the parameter $$\lambda $$ λ . Moreover, we produce minimal positive solutions and determine the monotonicity and continuity properties of the minimal positive solution map.

scholarly journals Functional Differential Inequalities with Unbounded Delay

2005 ◽  
Vol 12 (2) ◽  
pp. 237-254
Author(s):  
Zdzisław Kamont ◽  
Adam Nadolski
Keyword(s):  
Differential Inequality ◽  
Continuous Dependence ◽  
Functional Differential Equations ◽  
Uniqueness Result ◽  
Classical Solutions ◽  
Differential Inequalities ◽  
Unbounded Delay ◽  
Several Variables ◽  
Functional Differential ◽  
Continuous Dependence Of Solutions

Abstract We prove that a function of several variables satisfying a functional differential inequality with unbounded delay can be estimated by a solution of a suitable initial problem for an ordinary functional differential equation. As a consequence of the comparison theorem we obtain a Perron-type uniqueness result and a result on continuous dependence of solutions on given functions for partial functional differential equations with unbounded delay. We consider classical solutions on the Haar pyramid.

On a differential inequality

Analysis ◽  
2008 ◽  
Vol 28 (3) ◽  
Author(s):  
Richard Fournier
Keyword(s):  
Differential Inequality ◽  
Extremal Functions ◽  
Differential Inequalities

We identify the extremal functions for a class of differential inequalities first introduced by Sanford S. Miller and P. T. Mocanu in 1978.

scholarly journals Starlikeness of meromorphic functions involving certain differential inequalities

2021 ◽  
Vol 5 (1) ◽  
pp. 64-68
Author(s):  
Kuldeep Kaur Shergill ◽  
◽  
Sukhwinder Singh Billing ◽  
Keyword(s):  
Unit Disk ◽  
Differential Inequality ◽  
Meromorphic Functions ◽  
Differential Inequalities ◽  
Bazilevic Functions ◽  
New Criteria

In the present paper, we define a class of non-Bazilevic functions in punctured unit disk and study a differential inequality to obtain certain new criteria for starlikeness of meromorphic functions.

scholarly journals Solvability of a New q-Differential Equation Related to q-Differential Inequality of a Special Type of Analytic Functions

2021 ◽  
Vol 5 (4) ◽  
pp. 228
Author(s):  
Ibtisam Aldawish ◽  
Rabha W. Ibrahim
Keyword(s):  
Differential Equation ◽  
Differential Operator ◽  
Analytic Functions ◽  
Differential Inequality ◽  
Laguerre Polynomial ◽  
Analytic Solutions ◽  
Confluent Hypergeometric Function ◽  
Differential Inequalities ◽  
Quantum Calculus

The current study acts on the notion of quantum calculus together with a symmetric differential operator joining a special class of meromorphic multivalent functions in the puncher unit disk. We formulate a quantum symmetric differential operator and employ it to investigate the geometric properties of a class of meromorphic multivalent functions. We illustrate a set of differential inequalities based on the theory of subordination and superordination. In this real case study, we found the analytic solutions of q-differential equations. We indicate that the solutions are given in terms of confluent hypergeometric function of the second type and Laguerre polynomial.

The Eigenvalue Problem and Saint-Venant Decay Rate for a Nonhomogeneous Semi-Infinite Strip in Plane Strain

2013 ◽  
Vol 706-708 ◽  
pp. 1822-1826
Author(s):  
Qing Yang ◽  
Kai Zhang ◽  
Bai Lin Zheng ◽  
Jian Xin Zhu
Keyword(s):  
Numerical Calculation ◽  
Eigenvalue Problem ◽  
Decay Rate ◽  
Plane Strain ◽  
Plane Problem ◽  
Significant Influence ◽  
Positive Eigenvalue ◽  
Infinite Strip ◽  
Homogeneous Plane

The eigenvalue problem referring to a nonhomogeneous semi-infinite strip in plane strain is investigated here, by using the analogous methodology proposed by Papkovich and Fadle in homogeneous plane problem. Two types of nonhomogeneity are considered: (i) the modulus varies with the thickness coordinate exponentially, (ii) it varies with the length coordinate exponentially. The eigenvalues for these two cases are obtained by numerical calculation. By considering the smallest positive eigenvalue, the Saint-Venant Decay rate of the problem is estimated, which indicates material nonhomogeneity can have a significant influence on the Saint-Venant decay rate.

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