Comparison of solutions and successive approximations in the theory of the equation ∂2z/∂x∂y=f(x,y,z,∂z/∂x,∂z/∂y)
J. Kisyński ; A. Pelczar
GDML_Books, (1970), p.

CONTENTSIntroduction........................................................................................................................................................................................................... 5I. THE CAUCHY-DARBOUX PROBLEM IN FUNCTION CLASSES C1'*(Δa,b;E) AND L11,*(Δa,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 M1, (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

EUDML-ID : urn:eudml:doc:268455 
@book{bwmeta1.element.desklight-1c2e6c49-e4cd-4c60-8976-0f2e56929ef0,
     author = {J. Kisy\'nski and A. Pelczar},
     title = {Comparison of solutions and successive approximations in the theory of the equation $$\partial$^2z/$\partial$x$\partial$y = f(x, y, z, $\partial$z/$\partial$x, $\partial$z/$\partial$y)$
            },
     series = {GDML\_Books},
     publisher = {Instytut Matematyczny Polskiej Akademi Nauk},
     address = {Warszawa},
     year = {1970},
     zbl = {0219.35057},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.desklight-1c2e6c49-e4cd-4c60-8976-0f2e56929ef0}
}

J. Kisyński; A. Pelczar. Comparison of solutions and successive approximations in the theory of the equation $∂^2z/∂x∂y = f(x, y, z, ∂z/∂x, ∂z/∂y)$
            . GDML_Books (1970),  http://gdmltest.u-ga.fr/item/bwmeta1.element.desklight-1c2e6c49-e4cd-4c60-8976-0f2e56929ef0/