Unique solvability of a linear problem with perturbed periodic boundary values

Mehri, Bahman, and Nojumi, Mohammad H.. "Unique solvability of a linear problem with perturbed periodic boundary values." Czechoslovak Mathematical Journal 49.2 (1999): 351-362. <http://eudml.org/doc/30490>.

@article{Mehri1999,
abstract = {We investigate the problem with perturbed periodic boundary values \[ \left\rbrace \begin\{array\}\{ll\}y^\{\prime \prime \prime \}(x) + a\_2(x) y^\{\prime \prime \}(x) + a\_1(x) y^\{\prime \}(x) + a\_0(x) y(x) = f(x) , y^\{(i)\}(T) = c y^\{(i)\}(0), \ i = 0, 1, 2; \ 0 < c < 1 \end\{array\}\right.\] with $a_2, a_1, a_0 \in C[0,T]$ for some arbitrary positive real number $T$, by transforming the problem into an integral equation with the aid of a piecewise polynomial and utilizing the Fredholm alternative theorem to obtain a condition on the uniform norms of the coefficients $a_2$, $a_1$ and $a_0$ which guarantees unique solvability of the problem. Besides having theoretical value, this problem has also important applications since decay is a phenomenon that all physical signals and quantities (amplitude, velocity, acceleration, curvature, etc.) experience.},
author = {Mehri, Bahman, Nojumi, Mohammad H.},
journal = {Czechoslovak Mathematical Journal},
keywords = {Ordinary differential equations; integral equations; periodic boundary value problems; ordinary differential equations; integral equations; periodic boundary value problems},
language = {eng},
number = {2},
pages = {351-362},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Unique solvability of a linear problem with perturbed periodic boundary values},
url = {http://eudml.org/doc/30490},
volume = {49},
year = {1999},
}

TY - JOUR
AU - Mehri, Bahman
AU - Nojumi, Mohammad H.
TI - Unique solvability of a linear problem with perturbed periodic boundary values
JO - Czechoslovak Mathematical Journal
PY - 1999
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 49
IS - 2
SP - 351
EP - 362
AB - We investigate the problem with perturbed periodic boundary values \[ \left\rbrace \begin{array}{ll}y^{\prime \prime \prime }(x) + a_2(x) y^{\prime \prime }(x) + a_1(x) y^{\prime }(x) + a_0(x) y(x) = f(x) , y^{(i)}(T) = c y^{(i)}(0), \ i = 0, 1, 2; \ 0 < c < 1 \end{array}\right.\] with $a_2, a_1, a_0 \in C[0,T]$ for some arbitrary positive real number $T$, by transforming the problem into an integral equation with the aid of a piecewise polynomial and utilizing the Fredholm alternative theorem to obtain a condition on the uniform norms of the coefficients $a_2$, $a_1$ and $a_0$ which guarantees unique solvability of the problem. Besides having theoretical value, this problem has also important applications since decay is a phenomenon that all physical signals and quantities (amplitude, velocity, acceleration, curvature, etc.) experience.
LA - eng
KW - Ordinary differential equations; integral equations; periodic boundary value problems; ordinary differential equations; integral equations; periodic boundary value problems
UR - http://eudml.org/doc/30490
ER -