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Solvability of functional differential equations with multi-point boundary value problems at resonance. (English) Zbl 1142.34357
Summary: We discuss the following third order functional differential equations x '''(t) =f(t,x(t),(Fx)(t),x ' (t),(Gx ' )(t),x '' (t),(Hx '' )(t)), t[0,1], subject to the boundary conditions x(0)=0, x '' (0)=0, x ' (1)= i=1 m-2 α i x ' (η i ), where f:[0,1]× 6 , F,G,H are three operators, α i (i=1,,m-2)0, 0<η 1 <η 2 <<η m-2 <1. Under some appropriate conditions, some existence and multiplicity results are given for the problem at resonance by using a priori estimates and the topological degree theory of Mawhin.
MSC:
34K10Boundary value problems for functional-differential equations
34B10Nonlocal and multipoint boundary value problems for ODE
References:
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