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).
@article{bwmeta1.element.bwnjournal-article-apmv59z3p225bwm,
author = {Svatoslav Stan\v ek},
title = {On a class of functional boundary value problems for the equation x'' = f(t,x,x',x'',$\lambda$)},
journal = {Annales Polonici Mathematici},
volume = {60},
year = {1994},
pages = {225-237},
zbl = {0808.34025},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-apmv59z3p225bwm}
}
Svatoslav Staněk. On a class of functional boundary value problems for the equation x'' = f(t,x,x',x'',λ). Annales Polonici Mathematici, Tome 60 (1994) pp. 225-237. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-apmv59z3p225bwm/
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