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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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