The purpose of this paper is to study a class of ill-posed differential equations. In some settings, these differential equations exhibit uniqueness but not existence, while in others they exhibit existence but not uniqueness. An example of such a differential equation is, for a polynomial and continuous functions ,
These differential equations are related to inverse problems.
Submitted January 7, 2017. Published September 21, 2017.
Math Subject Classifications: 34K29, 34K09.
Key Words: Ill-posed; differential equation with difference quotient; existence without uniqueness; uniqueness without existence; inverse problem.
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| Brian Street |
University of Wisconsin-Madison
Department of Mathematics
480 Lincoln Dr.
Madison, WI 53706, USA
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