Convergence results for unbounded solutions of first order non-linear differential-functional equations
Henryk Leszczyński
Annales Polonici Mathematici, Tome 63 (1996), p. 1-16 / Harvested from The Polish Digital Mathematics Library

We consider the Cauchy problem in an unbounded region for equations of the type either Dtz(t,x)=f(t,x,z(t,x),z(t,x),Dxz(t,x)) or Dtz(t,x)=f(t,x,z(t,x),z,Dxz(t,x)). We prove convergence of their difference analogues by means of recurrence inequalities in some wide classes of unbounded functions.

Publié le : 1996-01-01
EUDML-ID : urn:eudml:doc:269997
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     author = {Henryk Leszczy\'nski},
     title = {Convergence results for unbounded solutions of first order non-linear differential-functional equations},
     journal = {Annales Polonici Mathematici},
     volume = {63},
     year = {1996},
     pages = {1-16},
     zbl = {0863.35110},
     language = {en},
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Henryk Leszczyński. Convergence results for unbounded solutions of first order non-linear differential-functional equations. Annales Polonici Mathematici, Tome 63 (1996) pp. 1-16. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-apmv64z1p1bwm/

[000] [1] P. Besala, On solutions of first order partial differential equations defined in an unbounded zone, Bull. Acad. Polon. Sci. 12 (1964), 95-99. | Zbl 0151.14304

[001] [2] P. Besala, Finite difference approximation to the Cauchy problem for non-linear parabolic differential equations, Ann. Polon. Math. 46 (1985), 19-26. | Zbl 0601.65073

[002] [3] Z. Kamont, On the Cauchy problem for system of first order partial differential equations, Serdica 5 (1979), 327-339. | Zbl 0446.35029

[003] [4] M. Krzyżański, Partial Differential Equations of Second Order, PWN, Warszawa, 1971.

[004] [5] H. Leszczyński, General finite difference approximation to the Cauchy problem for non-linear parabolic differential-functional equations, Ann. Polon. Math. 53 (1991), 15-28. | Zbl 0731.65079

[005] [6] H. Leszczyński, Uniqueness results for unbounded solutions of first order non-linear differential-functional equations, Acta Math. Hungar. 64 (1994), 75-92. | Zbl 0804.35137

[006] [7] M. Malec et A. Schiaffino, Méthode aux différences finies pour une équation non-linéaire différentielle fonctionnelle du type parabolique avec une condition initiale de Cauchy, Boll. Un. Mat. Ital. (7) 1-B (1987), 99-109. | Zbl 0617.65083

[007] [8] K. Prządka, Difference methods for non-linear partial differential functional equations of the first order, Math. Nachr. 138 (1988), 105-123. | Zbl 0668.65093

[008] [9] J. Szarski, Differential Inequalities, PWN, Warszawa, 1967.