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

Annales Polonici Mathematici (1994)

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

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topSvatoslav 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

top- [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] P. Hartman, Ordinary Differential Equations, Wiley-Interscience, New York, 1964. Zbl0125.32102
- [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] 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] 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] 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] 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] 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] S. Staněk, Leray-Schauder degree method in functional boundary problems depending on the parameter, Math. Nachr. 164 (1993), 333-344. Zbl0805.34053
- [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] 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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