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Technical Report 100


Recently a new class of differential equations, called differential equations of Sobolev type was studied in [4] in which an existence theorem of Picards type was investigated as well as a variation of constants formula. In [5], existence and comparison results for a class of Volterra integral equation of Sobolev-type were discussed. In this paper we recall the Peano type existence result from [5] for Sobolev-differential equations and show that solutions can be extended to the entire square under consideration. This result extends results found in [1] for nonlinear Volterra integral equations. Our results include a comparison result in addition to the usual type of differential inequalities, and a differential inequality theorem such as Müller's [6]. This in turn proves the existence of extremal solutions. For special cases of the above results see [2,3,7]


Mathematics | Physical Sciences and Mathematics

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Mathematics Commons



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