Publication detail
Singular Antiperiodic Boundary Value Problem with Given Maximal Values for Solutions
PŘIBYL, O. STANĚK, S.
Original Title
Singular Antiperiodic Boundary Value Problem with Given Maximal Values for Solutions
Type
journal article - other
Language
English
Original Abstract
The singular boundary value problem $(\phi(x'))' + \mu f(t,x,x')=0$, $x(0)+x(T)=0$, $x'(0)+x'(T)=0$, $\max\{x(t): 0 \le t \le T\}=A$ depending on the parameter $\mu$ is considered. Here the function $f$ satisfies local Carath\'eodory conditions on $[0,T] \times (\R\setminus \{0\})^2$ and $f$ may be singular at the zero value of its phase variables. The paper presents conditions which guarantee that for any $A>0$ there exists $\mu_A >0$ such that the above problem with $\mu=\mu_A$ has a solution. The proofs are based on regularization and sequential techniques and use the Leray-Schauder degree.
Keywords
Singular boundary value problem, antiperiodic boundary conditions, dependence on a parameter, $\phi$-Laplacian, existence, Leray-Schauder degree.
Authors
PŘIBYL, O.; STANĚK, S.
Released
1. 6. 2007
Publisher
Functional Differential Equations
ISBN
0793-1786
Periodical
Functional Differential Equations
Year of study
14
Number
2/4
State
State of Israel
Pages from
103
Pages to
114
Pages count
12
BibTex
@article{BUT44364,
author="Oto {Přibyl} and Svatoslav {Staněk}",
title="Singular Antiperiodic Boundary Value Problem with Given Maximal Values for Solutions",
journal="Functional Differential Equations",
year="2007",
volume="14",
number="2/4",
pages="103--114",
issn="0793-1786"
}