Leray-Schauder degree method in one-parameter functional boundary value problem
Abstract
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.
Keywords
one-parameter boundary value problem; existence of solutions; Leray-Schauder degree; Borsuk theorem
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Department of Mathematical Analysis, Faculty of Science, Palacký Univeristy, Czech Republic Czechia
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