# Existence of multiple solutions for some functional boundary value problems

Archivum Mathematicum (1992)

- Volume: 028, Issue: 1-2, page 57-65
- ISSN: 0044-8753

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topStaněk, Svatoslav. "Existence of multiple solutions for some functional boundary value problems." Archivum Mathematicum 028.1-2 (1992): 57-65. <http://eudml.org/doc/247344>.

@article{Staněk1992,

abstract = {Let $X$ be the Banach space of $C^0$-functions on $\langle 0,1\rangle $ with the sup norm and $\alpha ,\beta \in X \rightarrow \{R\}$ be continuous increasing functionals, $\alpha (0)= \beta (0)=0$. This paper deals with the functional differential equation (1) $x^\{\prime \prime \prime \} (t) = Q [ x, x^\prime , x^\{\prime \prime \}(t)] (t)$, where $Q:\{X\}^2 \times \{R\} \rightarrow \{X\}$ is locally bounded continuous operator. Some theorems about the existence of two different solutions of (1) satisfying the functional boundary conditions $\alpha (x)=0=\beta (x^\prime )$, $x^\{\prime \prime \}(1)-x^\{\prime \prime \}(0)=0$ are given. The method of proof makes use of Schauder linearizatin technique and the Schauder fixed point theorem. The results are modified for 2nd order functional differential equations.},

author = {Staněk, Svatoslav},

journal = {Archivum Mathematicum},

keywords = {Schauder linearization technique; Schauder differential equation; functional boundary conditions; boundary value problem; third order functional-differential equation; functional boundary conditions; Schauder's fixed point theorem; a priori estimates; degree theory; lower and upper solutions},

language = {eng},

number = {1-2},

pages = {57-65},

publisher = {Department of Mathematics, Faculty of Science of Masaryk University, Brno},

title = {Existence of multiple solutions for some functional boundary value problems},

url = {http://eudml.org/doc/247344},

volume = {028},

year = {1992},

}

TY - JOUR

AU - Staněk, Svatoslav

TI - Existence of multiple solutions for some functional boundary value problems

JO - Archivum Mathematicum

PY - 1992

PB - Department of Mathematics, Faculty of Science of Masaryk University, Brno

VL - 028

IS - 1-2

SP - 57

EP - 65

AB - Let $X$ be the Banach space of $C^0$-functions on $\langle 0,1\rangle $ with the sup norm and $\alpha ,\beta \in X \rightarrow {R}$ be continuous increasing functionals, $\alpha (0)= \beta (0)=0$. This paper deals with the functional differential equation (1) $x^{\prime \prime \prime } (t) = Q [ x, x^\prime , x^{\prime \prime }(t)] (t)$, where $Q:{X}^2 \times {R} \rightarrow {X}$ is locally bounded continuous operator. Some theorems about the existence of two different solutions of (1) satisfying the functional boundary conditions $\alpha (x)=0=\beta (x^\prime )$, $x^{\prime \prime }(1)-x^{\prime \prime }(0)=0$ are given. The method of proof makes use of Schauder linearizatin technique and the Schauder fixed point theorem. The results are modified for 2nd order functional differential equations.

LA - eng

KW - Schauder linearization technique; Schauder differential equation; functional boundary conditions; boundary value problem; third order functional-differential equation; functional boundary conditions; Schauder's fixed point theorem; a priori estimates; degree theory; lower and upper solutions

UR - http://eudml.org/doc/247344

ER -

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