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Zbl 0853.34062
Rachuunková, Irena; Staněk, Svatoslav
Topological degree method in functional boundary value problems at resonance. (English)
[J] Nonlinear Anal., Theory Methods Appl. 27, No.3, 271-285 (1996). ISSN 0362-546X

Sufficient conditions are obtained for the existence of solutions of second order functional differential equations of the form $x''(t) = f(t,x(t), (Fx) (t), x'(t), (Hx') (t))$, $t \in [0, 1]$, satisfying one of the boundary conditions $x'(0) = 0$, $x'(1) = 0$ or $x(0) = x(1)$, $x' (0) = x'(1)$, where $f : [0,1] \times\bbfR^4 \to\bbfR$ and $F,H \in {\cal D}$, ${\cal D}$ being the set of all operators $K : C([0,1],\bbfR) \to C ([0,1],\bbfR)$ which are continuous and bounded. The proofs of the results in this paper are based on the Mawhin continuation theorem [see {\it J. Mawhin}, Topological degree methods in nonlinear boundary value problems, AMS, Providence, R. I. (1979; Zbl 0414.34025)]. Some examples are given to illustrate the results.
[N.Parhi (Berhampur)]

MSC 2000:: *34K10 Boundary value problems for functional-differential equations

Keywords: second order functional differential equations; boundary conditions; Mawhin continuation theorem

Citations: Zbl 0414.34025

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