On a class of functional boundary value problems for the equation x'' = f(t,x,x',x'',λ)
Tom 59 / 1994
Annales Polonici Mathematici 59 (1994), 225-237
DOI: 10.4064/ap-59-3-225-237
Streszczenie
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).
