scholarly journals CHARACTERISTIC NUMBERS OF NON‐AUTONOMOUS EMDEN‐FOWLER TYPE EQUATIONS

2006 ◽  
Vol 11 (3) ◽  
pp. 243-252 ◽  
Author(s):  
A. Gritsans ◽  
F. Sadyrbaev
Keyword(s):  
Continuous Function ◽  
Boundary Value Problem ◽  
Extremal Problem ◽  
Boundary Value ◽  
Characteristic Number ◽  
Characteristic Numbers ◽  
All Solutions ◽  
Fowler Equation ◽  
Respective Solution

We consider the Emden‐Fowler equation x” = ‐q(t)|x|2εx, ε > 0, in the interval [a,b]. The coefficient q(t) is a positive valued continuous function. The Nehari characteristic number An associated with the Emden‐Fowler equation coincides with a minimal value of the functional [] over all solutions of the boundary value problem x” = ‐q(t)|x|2εx, x(a) = x(b) = 0, x(t) has exactly (n ‐ 1) zeros in (a, b). The respective solution is called the Nehari solution. We construct an example which shows that the Nehari extremal problem may have more than one solution.

scholarly journals Existence and Exact Asymptotic Behavior of Positive Solutions for a Fractional Boundary Value Problem

2013 ◽  
Vol 2013 ◽  
pp. 1-6 ◽  
Author(s):  
Habib Mâagli ◽  
Noureddine Mhadhebi ◽  
Noureddine Zeddini
Keyword(s):  
Asymptotic Behavior ◽  
Continuous Function ◽  
Boundary Value Problem ◽  
Positive Solution ◽  
Positive Solutions ◽  
Existence And Uniqueness ◽  
Boundary Value ◽  
Fractional Boundary Value Problem ◽  
Exact Asymptotic Behavior ◽  
Nonnegative Continuous Function

We establish the existence and uniqueness of a positive solution for the fractional boundary value problem , with the condition , where , and is a nonnegative continuous function on that may be singular at or .

scholarly journals Existence and Estimates of Positive Solutions for Some Singular Fractional Boundary Value Problems

2014 ◽  
Vol 2014 ◽  
pp. 1-7 ◽  
Author(s):  
Habib Mâagli ◽  
Noureddine Mhadhebi ◽  
Noureddine Zeddini
Keyword(s):  
Continuous Function ◽  
Boundary Value Problem ◽  
Boundary Value Problems ◽  
Positive Solution ◽  
Existence And Uniqueness ◽  
Boundary Value ◽  
Global Behavior ◽  
Fractional Boundary Value Problem ◽  
Nonnegative Continuous Function ◽  
Fractional Boundary Value Problems

We establish the existence and uniqueness of a positive solutionufor the following fractional boundary value problem:Dαu(x)=−a(x)uσ(x),x∈(0,1)with the conditionslimx→0+⁡x2−αu(x)=0,u(1)=0, where1<α≤2,σ∈(−1,1), andais a nonnegative continuous function on(0,1)that may be singular atx=0orx=1. We also give the global behavior of such a solution.

scholarly journals Lyapunov-Type Inequalities for a Conformable Fractional Boundary Value Problem of Order 3<α≤4

2019 ◽  
Vol 2019 ◽  
pp. 1-5 ◽  
Author(s):  
Imed Bachar ◽  
Hassan Eltayeb
Keyword(s):  
Continuous Function ◽  
Eigenvalue Problem ◽  
Boundary Value Problem ◽  
Fractional Derivative ◽  
Boundary Value ◽  
Conformable Fractional Derivative ◽  
Fractional Boundary Value Problem

We establish new Lyapunov-type inequalities for the following conformable fractional boundary value problem (BVP): Tαaut+q(t)u(t)=0,  a<t<b,  u(a)=u′(a)=u′′(a)=u′′(b)=0, where Tαa is the conformable fractional derivative of order α∈(3,4] and q is a real-valued continuous function. Some applications to the corresponding eigenvalue problem are discussed.

scholarly journals On third-order three-point right focal boundary value problems

2008 ◽  
Vol 39 (4) ◽  
pp. 317-324
Author(s):  
Xiangyun Wu ◽  
Zhanbing Bai
Keyword(s):  
Fixed Point ◽  
Continuous Function ◽  
Fixed Point Theorem ◽  
Boundary Value Problem ◽  
Boundary Value ◽  
Point Boundary ◽  
Third Order ◽  
First Order ◽  
Existence Of Positive Solutions ◽  
Nonnegative Continuous Function

In this paper, a fixed point theorem in a cone, some inequalities of the associated Green's function and the concavity of solutions are applied to obtain the existence of positive solutions of third-order three-point boundary value problem with dependence on the first-order derivative$\begin{cases}& x'''(t) = f(t, x(t), x'(t)), \quad 0 < t < 1, \\ & x(0) = x'(\eta) = x''(1) = 0, \end{cases}$where $f:[0, 1]\times[0, \infty)\times R\to [0,\infty)$ is a nonnegative continuous function, $\eta\in(1/2, 1).$

scholarly journals Solvability of some boundary value problems involving p-Laplacian and non-autonomous differential operators

2019 ◽  
Vol 2019 (1) ◽  
Author(s):  
Milena Petrini
Keyword(s):  
Continuous Function ◽  
Boundary Value Problem ◽  
Existence Result ◽  
Differential Operators ◽  
Existence Of Solutions ◽  
Boundary Value ◽  
Nonlinear Function ◽  
Laplacian Operator ◽  
Positive Continuous Function ◽  
The Relationship

AbstractThe paper deals with the existence and non-existence of solutions of the following nonlinear non-autonomous boundary value problem governed by the p-Laplacian operator: $$(P) \quad \textstyle\begin{cases} (h(t,x(t)) \vert x'(t) \vert ^{p-2} x'(t))' = g(t,x(t),x'(t)) \quad \text{a.e. } t\in \mathbb{R}, \\ x(-\infty )=a, \qquad x(+\infty )= b \end{cases} $$(P){(h(t,x(t))|x′(t)|p−2x′(t))′=g(t,x(t),x′(t))a.e. t∈R,x(−∞)=a,x(+∞)=b with $a< b$a<b, where a is a positive, continuous function and g is a Caratheódory nonlinear function.We prove an existence result, underlying the relationship between the behavior of $g(t,x,\cdot )$g(t,x,⋅) as $y\to 0$y→0 related to that of $g(\cdot ,x,y)$g(⋅,x,y) and $h(\cdot ,x) $h(⋅,x) as $|t|\to +\infty $|t|→+∞.

Sign in / Sign up

Export Citation Format

Share Document