Geodesic
On a class of functional boundary value problems for the equation x'' = f(t,x,x',x'',λ)
Annales Polonici Mathematici, Tome 59 (1994) no. 3, pp. 225-237.

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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).
DOI : 10.4064/ap-59-3-225-237
Keywords: Leray-Schauder degree theory, functional boundary conditions, boundary value problem depending on the parameter

Svatoslav Staněk 1

1 
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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, Tome 59 (1994) no. 3, pp. 225-237. doi : 10.4064/ap-59-3-225-237. http://geodesic.mathdoc.fr/articles/10.4064/ap-59-3-225-237/

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