We consider the Cauchy problem in an unbounded region for equations of the type either or . We prove convergence of their difference analogues by means of recurrence inequalities in some wide classes of unbounded functions.
@article{bwmeta1.element.bwnjournal-article-apmv64z1p1bwm, 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}, url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-apmv64z1p1bwm} }
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.