On a class of functional boundary value problems for the equation x'' = f(t,x,x',x'',λ)

Svatoslav Staněk

Annales Polonici Mathematici (1994)

  • Volume: 59, Issue: 3, page 225-237
  • ISSN: 0066-2216

Abstract

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The Leray-Schauder degree theory is used to obtain sufficient conditions for the existence and uniqueness of solutions for the boundary value problem x'' = f(t,x,x',x'',λ), α(x) = 0, β(x̅) = 0, γ(x̿)=0, depending on the parameter λ. Here α, β, γ are linear bounded functionals defined on the Banach space of C⁰-functions on [0,1] and x̅(t) = x(0) - x(t), x̿(t)=x(1)-x(t).

How to cite

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Svatoslav Staněk. "On a class of functional boundary value problems for the equation x'' = f(t,x,x',x'',λ)." Annales Polonici Mathematici 59.3 (1994): 225-237. <http://eudml.org/doc/262407>.

@article{SvatoslavStaněk1994,
abstract = {The Leray-Schauder degree theory is used to obtain sufficient conditions for the existence and uniqueness of solutions for the boundary value problem x'' = f(t,x,x',x'',λ), α(x) = 0, β(x̅) = 0, γ(x̿)=0, depending on the parameter λ. Here α, β, γ are linear bounded functionals defined on the Banach space of C⁰-functions on [0,1] and x̅(t) = x(0) - x(t), x̿(t)=x(1)-x(t).},
author = {Svatoslav Staněk},
journal = {Annales Polonici Mathematici},
keywords = {Leray-Schauder degree theory; functional boundary conditions; boundary value problem depending on the parameter; existence; uniqueness; boundary value problem},
language = {eng},
number = {3},
pages = {225-237},
title = {On a class of functional boundary value problems for the equation x'' = f(t,x,x',x'',λ)},
url = {http://eudml.org/doc/262407},
volume = {59},
year = {1994},
}

TY - JOUR
AU - Svatoslav Staněk
TI - On a class of functional boundary value problems for the equation x'' = f(t,x,x',x'',λ)
JO - Annales Polonici Mathematici
PY - 1994
VL - 59
IS - 3
SP - 225
EP - 237
AB - The Leray-Schauder degree theory is used to obtain sufficient conditions for the existence and uniqueness of solutions for the boundary value problem x'' = f(t,x,x',x'',λ), α(x) = 0, β(x̅) = 0, γ(x̿)=0, depending on the parameter λ. Here α, β, γ are linear bounded functionals defined on the Banach space of C⁰-functions on [0,1] and x̅(t) = x(0) - x(t), x̿(t)=x(1)-x(t).
LA - eng
KW - Leray-Schauder degree theory; functional boundary conditions; boundary value problem depending on the parameter; existence; uniqueness; boundary value problem
UR - http://eudml.org/doc/262407
ER -

References

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  1. [1] C. Fabry and P. Habets, The Picard boundary value problem for second order vector differential equations, J. Differential Equations 42 (1981), 186-198. Zbl0439.34018
  2. [2] P. Hartman, Ordinary Differential Equations, Wiley-Interscience, New York, 1964. Zbl0125.32102
  3. [3] W. V. Petryshyn, Solvability of various boundary value problems for the equation x'' = F(t,x,x',x'') - y, Pacific J. Math. 122 (1986), 169-195. Zbl0585.34020
  4. [4] S. Staněk, Three-point boundary value problem for nonlinear third-order differential equations with parameter, Acta Univ. Palack. Olomuc. Fac. Rerum Natur., 100, Math. 30 (1991), 61-74. Zbl0752.34019
  5. [5] S. Staněk, Multi-point boundary value problem for a class of functional differential equations with parameter, Math. Slovaca 42 (1992), 85-96. Zbl0745.34066
  6. [6] S. Staněk, Three-point boundary value problem for nonlinear second-order differential equation with parameter, Czechoslovak Math. J. 42 (117) (1992), 241-256. Zbl0779.34017
  7. [7] S. Staněk, On a class of five-point boundary value problems in second-order functional differential equations with parameter, Acta Math. Hungar. 62 (1993), 253-262. Zbl0801.34064
  8. [8] S. Staněk, On a class of functional boundary value problems for second-order functional differential equations with parameter, Czechoslovak Math. J. 43 (118) (1993), 339-348. Zbl0788.34069
  9. [9] S. Staněk, Leray-Schauder degree method in functional boundary problems depending on the parameter, Math. Nachr. 164 (1993), 333-344. Zbl0805.34053
  10. [10] S. Staněk, On certain three-point regular boundary value problems for nonlinear second-order differential equations depending on the parameter, 1992, submitted for publication. 
  11. [11] A. Tineo, Existence of solutions for a class of boundary value problems for the equation x'' = F(t,x,x',x''), Comment. Math. Univ. Carolin. 29 (1988), 285-291. Zbl0667.34026

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