scholarly journals Existence results for nonlinear problems with $\varphi$- Laplacian operators and nonlocal boundary conditions

2022 ◽  
Vol 40 ◽  
pp. 1-10
Author(s):  
Dionicio Pastor Dallos Santos
Keyword(s):  
Continuous Function ◽  
Real Number ◽  
Positive Real Number ◽  
Nonlocal Boundary ◽  
Degree Theory ◽  
Nonlinear Problems ◽  
Nonlocal Boundary Conditions ◽  
Existence Results ◽  
Positive Real ◽  
Laplacian Operators

Using Leray-Schauder degree theory we study the existence of at least one solution for the boundary value problem of the type\[\left\{\begin{array}{lll}(\varphi(u' ))' = f(t,u,u') & & \\u'(0)=u(0), \ u'(T)= bu'(0), & & \quad \quad \end{array}\right.\] where $\varphi: \mathbb{R}\rightarrow \mathbb{R}$ is a homeomorphism such that $\varphi(0)=0$, $f:\left[0, T\right]\times \mathbb{R} \times \mathbb{R}\rightarrow \mathbb{R} $ is a continuous function, $T$ a positive real number, and $b$ some non zero real number.

EIGENVALUE PROBLEMS ASSOCIATED WITH NONHOMOGENEOUS DIFFERENTIAL OPERATORS, IN ORLICZ–SOBOLEV SPACES

2008 ◽  
Vol 06 (01) ◽  
pp. 83-98 ◽  
Author(s):  
MIHAI MIHĂILESCU ◽  
VICENŢIU RĂDULESCU
Keyword(s):  
Continuous Function ◽  
Boundary Value Problem ◽  
Real Number ◽  
Bounded Domain ◽  
Sobolev Spaces ◽  
Positive Real Number ◽  
Differential Operators ◽  
Eigenvalue Problems ◽  
Smooth Boundary ◽  
Positive Real

We study the boundary value problem - div ((a1(|∇ u|) + a2(|∇ u|))∇ u) = λ|u|q(x)-2u in Ω, u = 0 on ∂Ω, where Ω is a bounded domain in ℝN (N ≥ 3) with smooth boundary, λ is a positive real number, q is a continuous function and a1, a2 are two mappings such that a1(|t|)t, a2(|t|)t are increasing homeomorphisms from ℝ to ℝ. We establish the existence of two positive constants λ0 and λ1 with λ0 ≤ λ1 such that any λ ∈ [λ1, ∞) is an eigenvalue, while any λ ∈ (0, λ0) is not an eigenvalue of the above problem.

scholarly journals Finding of principle square root of a real number by using interpolation method

2018 ◽  
Vol 7 (1) ◽  
pp. 77-83
Author(s):  
Rajendra Prasad Regmi
Keyword(s):  
Real Number ◽  
Positive Real Number ◽  
Interpolation Method ◽  
Square Root ◽  
Real Numbers ◽  
Positive Real ◽  
Unknown Quantity ◽  
Square Roots

There are various methods of finding the square roots of positive real number. This paper deals with finding the principle square root of positive real numbers by using Lagrange’s and Newton’s interpolation method. The interpolation method is the process of finding the values of unknown quantity (y) between two known quantities.

Some remarks on the solvability of non-local elliptic problems with the Hardy potential

2014 ◽  
Vol 16 (04) ◽  
pp. 1350046 ◽  
Author(s):  
B. Barrios ◽  
M. Medina ◽  
I. Peral
Keyword(s):  
Real Number ◽  
Sobolev Inequality ◽  
Positive Real Number ◽  
Fractional Power ◽  
Existence Of Solution ◽  
Sharp Constant ◽  
Hardy Potential ◽  
Positive Real ◽  
Existence And Multiplicity ◽  
Non Local

The aim of this paper is to study the solvability of the following problem, [Formula: see text] where (-Δ)s, with s ∈ (0, 1), is a fractional power of the positive operator -Δ, Ω ⊂ ℝN, N > 2s, is a Lipschitz bounded domain such that 0 ∈ Ω, μ is a positive real number, λ < ΛN,s, the sharp constant of the Hardy–Sobolev inequality, 0 < q < 1 and [Formula: see text], with αλ a parameter depending on λ and satisfying [Formula: see text]. We will discuss the existence and multiplicity of solutions depending on the value of p, proving in particular that p(λ, s) is the threshold for the existence of solution to problem (Pμ).

Ultradiversities and their spherical completeness

2020 ◽  
Vol 26 (2) ◽  
pp. 231-240
Author(s):  
Gholamreza H. Mehrabani ◽  
Kourosh Nourouzi
Keyword(s):  
Real Number ◽  
Finite Subset ◽  
Positive Real Number ◽  
Metric Spaces ◽  
Nonexpansive Mappings ◽  
Ultrametric Spaces ◽  
Positive Real

AbstractDiversities are a generalization of metric spaces which associate a positive real number to every finite subset of the space. In this paper, we introduce ultradiversities which are themselves simultaneously diversities and a sort of generalization of ultrametric spaces. We also give the notion of spherical completeness for ultradiversities based on the balls defined in such spaces. In particular, with the help of nonexpansive mappings defined between ultradiversities, we show that an ultradiversity is spherically complete if and only if it is injective.

Ballots, queues and random graphs

1989 ◽  
Vol 26 (1) ◽  
pp. 103-112 ◽  
Author(s):  
Lajos Takács
Keyword(s):  
Real Number ◽  
Random Graph ◽  
Random Graphs ◽  
Limit Distribution ◽  
Positive Real Number ◽  
Positive Real ◽  
Ballot Theorem

This paper demonstrates how a simple ballot theorem leads, through the interjection of a queuing process, to the solution of a problem in the theory of random graphs connected with a study of polymers in chemistry. Let Γn(p) denote a random graph with n vertices in which any two vertices, independently of the others, are connected by an edge with probability p where 0 < p < 1. Denote by ρ n(s) the number of vertices in the union of all those components of Γn(p) which contain at least one vertex of a given set of s vertices. This paper is concerned with the determination of the distribution of ρ n(s) and the limit distribution of ρ n(s) as n → ∞and ρ → 0 in such a way that np → a where a is a positive real number.

AN EXACT FORMULA FOR THE HARMONIC CONTINUED FRACTION

2020 ◽  
pp. 1-11
Author(s):  
MARTIN BUNDER ◽  
PETER NICKOLAS ◽  
JOSEPH TONIEN
Keyword(s):  
Real Number ◽  
Continued Fraction ◽  
Positive Real Number ◽  
Exact Formula ◽  
Positive Real ◽  
Image Position

For a positive real number $t$ , define the harmonic continued fraction $$\begin{eqnarray}\text{HCF}(t)=\biggl[\frac{t}{1},\frac{t}{2},\frac{t}{3},\ldots \biggr].\end{eqnarray}$$ We prove that $$\begin{eqnarray}\text{HCF}(t)=\frac{1}{1-2t(\frac{1}{t+2}-\frac{1}{t+4}+\frac{1}{t+6}-\cdots \,)}.\end{eqnarray}$$

scholarly journals Algebraic Numbers Satisfying Polynomials with Positive Rational Coefficients

2014 ◽  
Vol 2014 ◽  
pp. 1-8
Author(s):  
Vichian Laohakosol ◽  
Suton Tadee
Keyword(s):  
Growth Factor ◽  
Real Number ◽  
Algebraic Number ◽  
Positive Real Number ◽  
Algebraic Numbers ◽  
Positive Real ◽  
Quantitative Version

A theorem of Dubickas, affirming a conjecture of Kuba, states that a nonzero algebraic number is a root of a polynomial f with positive rational coefficients if and only if none of its conjugates is a positive real number. A certain quantitative version of this result, yielding a growth factor for the coefficients of f similar to the condition of the classical Eneström-Kakeya theorem of such polynomial, is derived. The bound for the growth factor so obtained is shown to be sharp for some particular classes of algebraic numbers.

Ballots, queues and random graphs

1989 ◽  
Vol 26 (01) ◽  
pp. 103-112 ◽  
Author(s):  
Lajos Takács
Keyword(s):  
Real Number ◽  
Random Graph ◽  
Random Graphs ◽  
Limit Distribution ◽  
Positive Real Number ◽  
Positive Real ◽  
Ballot Theorem

This paper demonstrates how a simple ballot theorem leads, through the interjection of a queuing process, to the solution of a problem in the theory of random graphs connected with a study of polymers in chemistry. Let Γ n (p) denote a random graph with n vertices in which any two vertices, independently of the others, are connected by an edge with probability p where 0 &lt; p &lt; 1. Denote by ρ n (s) the number of vertices in the union of all those components of Γ n (p) which contain at least one vertex of a given set of s vertices. This paper is concerned with the determination of the distribution of ρ n (s) and the limit distribution of ρ n (s) as n → ∞and ρ → 0 in such a way that np → a where a is a positive real number.

Using Logarithms to Explore Power and Exponential Functions

1994 ◽  
Vol 87 (3) ◽  
pp. 161-170
Author(s):  
James R. Rahn ◽  
Barry A. Berndes
Keyword(s):  
Experimental Data ◽  
Real Number ◽  
Positive Real Number ◽  
Power Functions ◽  
Exponential Functions ◽  
Positive Real ◽  
Nonzero Real Number ◽  
Physical Phenomena ◽  
The Relationship

Power functions and exponential functions often describe the relationship between variables in physical phenomena. Power functions are equations of the form y = kxn (see fig. 1), where k is a nonzero real number and n is a nonzero real number not equal to 1. Exponential functions are equations of the form y = kbx (see fig. 2), where k is a nonzero real number and b is a positive real number. Students should be able visually to recognize these functions so that they can easily identify their appearance when experimental data are graphed. When physical phenomena appear to describe exponential and power functions, logarithms can be used to locate approximate functions that represent the phenomena.

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