New a priori estimates for the solutions of two-point boundary-value problems and applications

1980 ◽  
Vol 21 (1) ◽  
pp. 85-93
Author(s):  
A. M. Krasnosel'skii
Keyword(s):  
Boundary Value Problems ◽  
A Priori Estimates ◽  
Boundary Value ◽  
A Priori ◽  
Point Boundary ◽  
Priori Estimates

A priori estimates of solutions of boundary value problems for two-dimensional systems of singular differential inequalities

2011 ◽  
Vol 18 (1) ◽  
pp. 163-175
Author(s):  
Nino Partsvania
Keyword(s):  
Boundary Value Problems ◽  
A Priori Estimates ◽  
Boundary Value ◽  
A Priori ◽  
Differential Inequalities ◽  
Two Dimensional ◽  
Point Boundary ◽  
Estimates Of Solutions ◽  
Priori Estimates ◽  
Singular Coefficients

Abstract A priori estimates of solutions of two-point boundary value problems for two-dimensional systems of differential inequalities with singular coefficients are established.

scholarly journals Boundary value problems with nonlocal conditions for hyperbolic systems of equations with two independent variables

2020 ◽  
Vol 53 (2) ◽  
pp. 159-180
Author(s):  
V. M. Kyrylych ◽  
O. Z. Slyusarchuk
Keyword(s):  
Boundary Value Problems ◽  
A Priori Estimates ◽  
Hyperbolic Systems ◽  
Boundary Value ◽  
A Priori ◽  
Nonlocal Boundary ◽  
Nonlocal Conditions ◽  
Mixed Problems ◽  
Priori Estimates ◽  
Smooth Coefficients

Nonlocal boundary value problems for arbitrary order hyperbolic systems with one spatial variable are considered. A priori estimates for general nonlocal mixed problems for systems with smooth and piecewise smooth coefficients are obtained. The correct solvability of such problems is proved.Examples of additional conditions necessity are provided.

On the well-posedness of boundary value problems for nonclassical differential equations of higher order

2017 ◽  
Vol 10 (03) ◽  
pp. 1750059
Author(s):  
N. R. Pinigina
Keyword(s):  
Boundary Value Problems ◽  
Spectral Parameter ◽  
A Priori Estimates ◽  
Boundary Value ◽  
A Priori ◽  
Fourier Method ◽  
Countable System ◽  
Priori Estimates ◽  
Complex Eigenvalues ◽  
Even Order

This paper investigates a high even-order nonclassical differential equation with a spectral parameter. We proved that this equation has a countable system of nontrivial solutions if spectral parameter is negative. We consider two cases, one where the spectral parameter is equal to eigenvalues and one where the spectral parameter is not equal to eigenvalues. In both cases, we proved the existence of regular solutions of boundary value problems for this equation. To do this, we combined the Fourier method and the method of a priori estimates. Moreover, we found some conditions for unsolvability of boundary value problems. In addition, for adjoint problems, we proved that there is no complex eigenvalues.

A priori estimates of the positive solution of the two-point boundary value problem for one second-order nonlinear differential equation

2019 ◽  
pp. 38-48
Author(s):  
Edelkhan Abduragimov
Keyword(s):  
Differential Equation ◽  
Boundary Value Problem ◽  
Positive Solution ◽  
Nonlinear Differential Equation ◽  
A Priori Estimates ◽  
Boundary Value ◽  
A Priori ◽  
Second Order ◽  
Point Boundary ◽  
Priori Estimates

A priori estimates of the positive solution of the two-point boundary value problem are obtained $y^{\prime\prime}=-f(x,y)$, $0<x<1$, $y(0)=y(1)=0$ assuming that $f(x,y)$ is continuous at $x \in [0,1]$, $y \in R$ and satisfies the condition $a_0 x^{\gamma}y^p \leq f(x,y) \leq a_1 y^p$, where $a_0>0$, $a_1>0$, $p>1$, $\gamma \geq 0$ -- constants.

Sign in / Sign up

Export Citation Format

Share Document