Comparison of solutions and successive approximations in the theory of the equation ${\partial }^{2}z/\partial x\partial y=f(x,y,z,\partial z/\partial x,\partial z/\partial y)$

J. Kisyński, and A. Pelczar. Comparison of solutions and successive approximations in the theory of the equation $∂^2z/∂x∂y = f(x, y, z, ∂z/∂x, ∂z/∂y)$. Warszawa: Instytut Matematyczny Polskiej Akademi Nauk, 1970. <http://eudml.org/doc/268455>.

@book{J1970,
abstract = {CONTENTSIntroduction........................................................................................................................................................................................................... 5I. THE CAUCHY-DARBOUX PROBLEM IN FUNCTION CLASSES $C^1^\{\prime \}*(Δ_\{a,b\};E)$ AND $L^\{1,*\}_1(Δ_\{a,b\};E)$......................... 71. Basic function classes ................................................................................................................................................................................... 72. The Cauchy-Darboux problem ...................................................................................................................................................................... 12II. Comparison of solutions ............................................................................................................................................................................... 183. The growth estimations.................................................................................................................................................................................. 184. Maximal solutions............................................................................................................................................................................................ 265. A theorem on extension of inequalities........................................................................................................................................................ 286. Effective estimation in the case $M_1$, (b)................................................................................................................................................. 30III. COMPARATIVE CRITERIA OF EXISTENCE AND UNIQUENESS OP SOLUTIONS OF THE CAUCHY-DARBOUX PROBLEM...................................................................................................................................................................................... 357. Basic classes of comparative functions...................................................................................................................................................... 358. Existence and uniqueness of solutions of the Cauchy-Darboux problem............................................................................................ 429. Remarks on the continuous dependence of solutions on boundary data and on the second member........................................ 4710. Examples......................................................................................................................................................................................................... 49BIBLIOGRAPHICAL REMARKS.......................................................................................................................................................................... 66BIBLIOGRAPHY..................................................................................................................................................................................................... 68INDEX OF SYMBOLS............................................................................................................................................................................................ 74},
author = {J. Kisyński, A. Pelczar},
language = {eng},
location = {Warszawa},
publisher = {Instytut Matematyczny Polskiej Akademi Nauk},
title = {Comparison of solutions and successive approximations in the theory of the equation $∂^2z/∂x∂y = f(x, y, z, ∂z/∂x, ∂z/∂y)$},
url = {http://eudml.org/doc/268455},
year = {1970},
}

TY - BOOK
AU - J. Kisyński
AU - A. Pelczar
TI - Comparison of solutions and successive approximations in the theory of the equation $∂^2z/∂x∂y = f(x, y, z, ∂z/∂x, ∂z/∂y)$
PY - 1970
CY - Warszawa
PB - Instytut Matematyczny Polskiej Akademi Nauk
AB - CONTENTSIntroduction........................................................................................................................................................................................................... 5I. THE CAUCHY-DARBOUX PROBLEM IN FUNCTION CLASSES $C^1^{\prime }*(Δ_{a,b};E)$ AND $L^{1,*}_1(Δ_{a,b};E)$......................... 71. Basic function classes ................................................................................................................................................................................... 72. The Cauchy-Darboux problem ...................................................................................................................................................................... 12II. Comparison of solutions ............................................................................................................................................................................... 183. The growth estimations.................................................................................................................................................................................. 184. Maximal solutions............................................................................................................................................................................................ 265. A theorem on extension of inequalities........................................................................................................................................................ 286. Effective estimation in the case $M_1$, (b)................................................................................................................................................. 30III. COMPARATIVE CRITERIA OF EXISTENCE AND UNIQUENESS OP SOLUTIONS OF THE CAUCHY-DARBOUX PROBLEM...................................................................................................................................................................................... 357. Basic classes of comparative functions...................................................................................................................................................... 358. Existence and uniqueness of solutions of the Cauchy-Darboux problem............................................................................................ 429. Remarks on the continuous dependence of solutions on boundary data and on the second member........................................ 4710. Examples......................................................................................................................................................................................................... 49BIBLIOGRAPHICAL REMARKS.......................................................................................................................................................................... 66BIBLIOGRAPHY..................................................................................................................................................................................................... 68INDEX OF SYMBOLS............................................................................................................................................................................................ 74
LA - eng
UR - http://eudml.org/doc/268455
ER -