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Generalized spaces of germs of smooth solutions of first-order equation and their relationship with the direct Lyapunov method. (English. Russian original) Zbl 0728.35011
Sov. Math. 34, No. 5, 56-62 (1990); translation from Izv. Vyssh. Uchebn. Zaved., Mat. 1990, No. 5(336), 47-53 (1990).
The author discusses the first order PDE $$F(x,p)=0$$ where $$x=(x_ 1,x_ 2,...,x_ n)$$, $$p=(z_{x_ 1},z_{x_ 2},...,z_{x_ n})$$, in order to study the Lyapunov stability and to construct Lyapunov functions.

##### MSC:
 35B35 Stability in context of PDEs 35F20 Nonlinear first-order PDEs
##### Keywords:
Lyapunov stability; Lyapunov functions