Partial Differential Equations
Springer, 1982 - 249 páginas
This book is a very well-accepted introduction to the subject. In it, the author identifies the significant aspects of the theory and explores them with a limited amount of machinery from mathematical analysis. Now, in this fourth edition, the book has again been updated with an additional chapter on Lewy 's example of a linear equation without solutions.
Resultados 1-3 de 68
These imply that bh ' – cg ' = 0 , ah ' – cf ' = 0 and hence that f ' , g ' , h ' are proportional to a , b , c . Hence J = 0 is incompatible with the existence of a solution unless I happens to be characteristic at So.
Now the last integral in ( 5.40 ) depends on a only through v , and hence * is a real analytic function of 1 for de ( a + € , j ) , 12 – 2 * / < 8. Hence 1 ( a ) is real analytic in a for 1 € ( a + E , u ) .
Then there exist roots j of ( 2.42 ) for all sufficiently large p for which Imu < -1/2 and hence roots i of ( 2.29 ) for which Im i < -py / 2 . This contradicts ( 2.30 ) for large p . Thus necessary for ( 2.30 ) is that the roots u of ...
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