Detail publikace

Singular Antiperiodic Boundary Value Problem with Given Maximal Values for Solutions

PŘIBYL, O. STANĚK, S.

Originální název

Singular Antiperiodic Boundary Value Problem with Given Maximal Values for Solutions

Typ

článek v časopise - ostatní, Jost

Jazyk

angličtina

Originální abstrakt

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.

Klíčová slova

Singular boundary value problem, antiperiodic boundary conditions, dependence on a parameter, $\phi$-Laplacian, existence, Leray-Schauder degree.

Autoři

PŘIBYL, O.; STANĚK, S.

Vydáno

1. 6. 2007

Nakladatel

Functional Differential Equations

ISSN

0793-1786

Periodikum

Functional Differential Equations

Ročník

14

Číslo

2/4

Stát

Stát Izrael

Strany od

103

Strany do

114

Strany počet

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"
}