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Leray-Schauder degree method in functional boundary value problems depending on the parameter. (English) Zbl 0805.34053
Summary: Using the Leray-Schauder degree method sufficient conditions for the one- parameter boundary value problem $$x'' = f(t,x,x', \lambda)$$, $$\alpha (x) = A$$, $$x(0) - x(1) = B$$, $$x'(0) - x'(1)=C$$, are stated. The application is given for a class of functional boundary value problems for nonlinear third-order functional differential equations depending on the parameter.

##### MSC:
 34K10 Boundary value problems for functional-differential equations 34B15 Nonlinear boundary value problems for ordinary differential equations
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##### References:
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