On the existence of one-signed periodic solutions of some differential equations of second order
Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica (2006)
- Volume: 45, Issue: 1, page 119-134
- ISSN: 0231-9721
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topLigęza, Jan. "On the existence of one-signed periodic solutions of some differential equations of second order." Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica 45.1 (2006): 119-134. <http://eudml.org/doc/32510>.
@article{Ligęza2006,
abstract = {We study the existence of one-signed periodic solutions of the equations \begin\{align\} & x^\{\prime \prime \} (t) - a^2(t) x(t) + \mu f(t, x(t), x^\{\prime \}(t)) = 0, & x^\{\prime \prime \}(t) + a^2(t) x(t) = \mu f(t, x(t), x^\{\prime \}(t)), \end\{align\}
where $ \mu > 0$, $a: (-\infty , +\infty ) \rightarrow (0, \infty ) $ is continuous and 1-periodic, $f$ is a continuous and 1-periodic in the first variable and may take values of different signs. The Krasnosielski fixed point theorem on cone is used.},
author = {Ligęza, Jan},
journal = {Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica},
keywords = {positive solutions; boundary value problems; cone; fixed point theorem},
language = {eng},
number = {1},
pages = {119-134},
publisher = {Palacký University Olomouc},
title = {On the existence of one-signed periodic solutions of some differential equations of second order},
url = {http://eudml.org/doc/32510},
volume = {45},
year = {2006},
}
TY - JOUR
AU - Ligęza, Jan
TI - On the existence of one-signed periodic solutions of some differential equations of second order
JO - Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica
PY - 2006
PB - Palacký University Olomouc
VL - 45
IS - 1
SP - 119
EP - 134
AB - We study the existence of one-signed periodic solutions of the equations \begin{align} & x^{\prime \prime } (t) - a^2(t) x(t) + \mu f(t, x(t), x^{\prime }(t)) = 0, & x^{\prime \prime }(t) + a^2(t) x(t) = \mu f(t, x(t), x^{\prime }(t)), \end{align}
where $ \mu > 0$, $a: (-\infty , +\infty ) \rightarrow (0, \infty ) $ is continuous and 1-periodic, $f$ is a continuous and 1-periodic in the first variable and may take values of different signs. The Krasnosielski fixed point theorem on cone is used.
LA - eng
KW - positive solutions; boundary value problems; cone; fixed point theorem
UR - http://eudml.org/doc/32510
ER -
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