Leray-Schauder degree method in one-parameter functional boundary value problem - Staněk, Svatoslav (Annales Mathematicae Silesianae, 1996)
Sufficient conditions for the existence of solutions of one-parameter functional boundary value problems of the type x" = f(t,x,xt,x',x't,λ), (x0,x'0) ∈ (ϕ,χ+c); c∈R, α(x|J) = A, β(x(T)-x|J) = B are given. Here f: J×R×Cr×R×Cr×R→R is continuous, ϕ,χ∈Cr, α,β are continuous increasing functionals, A,B∈R and x|J is the restriction of x to J=[0,T]. Results are proved by the Leray-Schauder degree method.