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Multiple nonnegative solutions of systems with coupled nonlinear boundary conditions. (English) Zbl 1312.34060

The authors present a theory for the existence of positive solution for a fairly general class of systems of ODEs subject to nonlinear, nonlocal boundary conditions (BCs). Using the theory of fixed point index, they investigated the existence and multiplicity of positive solutions for the perturbed Hammerstein integral equations. Then, the results are applied to coupled systems of boundary value problems.

MSC:

34B18 Positive solutions to nonlinear boundary value problems for ordinary differential equations
34B15 Nonlinear boundary value problems for ordinary differential equations
34B10 Nonlocal and multipoint boundary value problems for ordinary differential equations
47H30 Particular nonlinear operators (superposition, Hammerstein, Nemytskiĭ, Uryson, etc.)
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