Non-unique solutions of first order ordinary differential equations

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1937

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Valuable work has been done in the study of non-unique solutions of ordinary differential equations of the first order by Kamke, Osgood, Montel, Kneser, Fukunara, Naguno and others. In general these writers have considered differential equations in which the slope is a continuous function of the variables. Many of the results which the above mentioned authors have obtained under the assumption of continuity have recently been obtained by H. J. Ettlinger under much weaker assumptions. This thesis is an extension of Ettlinger's results and a treatment of the subject in part from the analysis situs point of view. Many new theorems not previously known, even for the continuous case, are thus obtained

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