A singular boundary value problem for odd-order differential equations |
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Authors: | Irena Rach?nková Svatoslav Staněk |
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Institution: | Department of Mathematical Analysis, Faculty of Science, Palacký University, Tomkova 40, 779 00 Olomouc, Czech Republic |
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Abstract: | The odd-order differential equation (−1)nx(2n+1)=f(t,x,…,x(2n)) together with the Lidstone boundary conditions x(2j)(0)=x(2j)(T)=0, 0?j?n−1, and the next condition x(2n)(0)=0 is discussed. Here f satisfying the local Carathéodory conditions can have singularities at the value zero of all its phase variables. Existence result for the above problem is proved by the general existence principle for singular boundary value problems. |
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Keywords: | Odd-order differential equation Singular boundary value problem Existence Regularization |
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