Solving nonstationary boundary value problems with piecewise linear boundary conditions for one-dimensional dynamics of deformable heteromodular elastic solid

2021 ◽  
Author(s):  
Olga V. Dudko ◽  
Anastasia A. Lapteva ◽  
Victoria E. Ragozina
Keyword(s):  
Boundary Conditions ◽  
Boundary Value Problems ◽  
Piecewise Linear ◽  
Boundary Value ◽  
Elastic Solid ◽  
Linear Boundary ◽  
One Dimensional ◽  
Nonstationary Boundary

scholarly journals Multi-point Taylor approximations in one-dimensional linear boundary value problems

2009 ◽  
Vol 207 (2) ◽  
pp. 519-527 ◽  
Author(s):  
José L. López ◽  
Ester Pérez Sinusía ◽  
Nico M. Temme
Keyword(s):  
Boundary Value Problems ◽  
Boundary Value ◽  
Linear Boundary ◽  
One Dimensional

scholarly journals The principal eigenvalue of some nth order linear boundary value problems

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Pedro Almenar ◽  
Lucas Jódar
Keyword(s):  
Integral Operator ◽  
Boundary Conditions ◽  
Boundary Value Problems ◽  
Boundary Value ◽  
Principal Eigenvalue ◽  
Green Functions ◽  
Linear Boundary ◽  
Order Linear

AbstractThe purpose of this paper is to present a procedure for the estimation of the smallest eigenvalues and their associated eigenfunctions of nth order linear boundary value problems with homogeneous boundary conditions defined in terms of quasi-derivatives. The procedure is based on the iterative application of the equivalent integral operator to functions of a cone and the calculation of the Collatz–Wielandt numbers of such functions. Some results on the sign of the Green functions of the boundary value problems are also provided.

scholarly journals Parametrization for some boundary value problems of interpolation type

2009 ◽  
Vol 43 (1) ◽  
pp. 229-242
Author(s):  
Miklós Rontó ◽  
Natalia Shchobak
Keyword(s):  
Boundary Value Problem ◽  
Boundary Conditions ◽  
Boundary Value Problems ◽  
Boundary Value ◽  
Analytic Form ◽  
Successive Approximations ◽  
Two Dimensional ◽  
Linear Boundary ◽  
Scalar Parameter ◽  
The Given

Abstract We obtain some results concerning the investigation of two-dimensional non-linear boundary value problems of interpolation type. We show that it is useful to reduce the given boundary value problem, using an appropriate substitution, to a parametrized boundary value problem containing some unknown scalar parameter in the boundary conditions. To study the transformed parametrized problem, we use a method which is based upon special types of successive approximations constructed in an analytic form.

scholarly journals Formulation of Problems for Stationary Dispersive Equations of Higher Orders on Bounded Intervals with General Boundary Conditions

2020 ◽  
Author(s):  
N. A. Larkin ◽  
J. Luchesi
Keyword(s):  
Boundary Conditions ◽  
Boundary Value Problems ◽  
Existence And Uniqueness ◽  
Boundary Value ◽  
Dispersive Equations ◽  
Linear Boundary ◽  
General Boundary Conditions ◽  
Regular Solutions ◽  
General Linear Boundary Conditions ◽  
Formulation Of Problems

Boundary value problems for linear stationary dispersive equations of order 2l + 1, l ∈ N with general linear boundary conditions have been considered on finite intervals (0, L). The existence and uniqueness of regular solutions have been established.

scholarly journals Existence of Three Positive Solutions form-Point Discrete Boundary Value Problems withp-Laplacian

2009 ◽  
Vol 2009 ◽  
pp. 1-15 ◽  
Author(s):  
Yanping Guo ◽  
Wenying Wei ◽  
Yuerong Chen
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Boundary Value Problem ◽  
Boundary Conditions ◽  
Boundary Value Problems ◽  
Positive Solutions ◽  
Point Theorem ◽  
Boundary Value ◽  
Laplacian Operator ◽  
One Dimensional

We consider the multi-point discrete boundary value problem with one-dimensionalp-Laplacian operatorΔ(ϕp(Δu(t−1))+q(t)f(t,u(t),Δu(t))=0,t∈{1,…,n−1}subject to the boundary conditions:u(0)=0,u(n)=∑i=1m−2aiu(ξi), whereϕp(s)=|s|p−2s,p>1,ξi∈{2,…,n−2}with1<ξ1<⋯<ξm−2<n−1andai∈(0,1),0<∑i=1m−2ai<1. Using a new fixed point theorem due to Avery and Peterson, we study the existence of at least three positive solutions to the above boundary value problem.

Uniqueness of positive solutions of some semilinear Sturm–Liouville problems on the half line

1984 ◽  
Vol 97 ◽  
pp. 259-263 ◽  
Author(s):  
J. F. Toland
Keyword(s):  
Boundary Conditions ◽  
Boundary Value Problems ◽  
Positive Solutions ◽  
Simple Proof ◽  
Boundary Value ◽  
Half Line ◽  
Linear Boundary ◽  
Autonomous Case ◽  
Sturm Liouville ◽  
Image Position

SynopsisThis note gives a simple proof of uniqueness for positive solutions of certain non-linear boundary value problems on ℝ+ which are typified by the equationwith boundary conditions u′(0) = u(+∞) = 0. In the autonomous case (r ≡ 1), this is easy to see, by quadrature. The proof here supposes r to be non-increasing on ℝ+.

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