Peano's Theorem for Implicit Differential Equations
Copyright policy )Peano's Theorem for Implicit Differential Equations
The author proves an existence result for the Cauchy problem \[ F(t,x,x', \ldots,x^{(m)})=0,\quad x(0)=x_0,x'(0)=x_1, \ldots, x^{(m-1)}(0)=x_{m-1}, \] with \(m \in {\mathbb N}\). He looks for solutions in the Lipschitz sense and gives an example where there exist no classical solutions. In the proofs, the viscosity lower and upper solutions method is used.
- Beijing Normal University China (People's Republic of)
- Yantai University China (People's Republic of)
- Department of Mathematics
- Beijing Normal University China (People's Republic of)
lower and upper solutions, Applied Mathematics, implicit differential equations, Initial value problems, existence, uniqueness, continuous dependence and continuation of solutions to ordinary differential equations, Peano's theorem, Analysis, Implicit ordinary differential equations, differential-algebraic equations
lower and upper solutions, Applied Mathematics, implicit differential equations, Initial value problems, existence, uniqueness, continuous dependence and continuation of solutions to ordinary differential equations, Peano's theorem, Analysis, Implicit ordinary differential equations, differential-algebraic equations
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