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Multiple solutions of nonlinear boundary value problems for two-dimensional differential systems

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  • This paper discusses the quasilinearization process, that is, reduction of a given boundary value problem to a quasi-linear one. Quasi-linear BVP has a solution of definite type which is induced by oscillatory properties of the linear part of a system. Conditions are given for a solution of a modified (quasi-linear) BVP to satisfy also the original problem. It is shown that multiple quasilinearizations with different linear parts if possible lead to multiple solutions.
    Mathematics Subject Classification: Primary: 34B15 .

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