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px941934

Single of nonlinear equations and eigenvalue differences

.) (9c) and because 0 = F (, SX0 +) a F (, zo + delete ) a F. (, SXo) + F (, 5D) a F. (,[link widoczny dla zalogowanych], O) a F (zo +) a F. ( 5 ) a DF. (, SXo) + DF. (, SX) a D (, 0) + F (, SX.) a F (, o) a 5D (, O) xo + DF (, O) xo a hF (, O) xD] + DF. (, O) w + as DhF. (, O) xD, (10) and (, ) - a DF (,) + D '. (, 0) x. Is a homeomorphism , so by ( 9), (10), there exists a constant > 0 such that K (ll + lI · l a I) ≤ f1 · h (11I1) + llD (,.) a D ( , 0) ll · llll + I5Ih (j5I) + · f a Ih (I a I). (11 ) is selected uo, so (, SXo +) ∈ Uo , there are (I1l1) <K / 4, h (I a I) <K / Z, DF (, o) a D (., o) ll </ 4. Then from (1 】 ), ( 12) I1f1 + II · I know a I ≤ 2h (II) · II / K. So that g (5) a 2h () / K, then for every oral ∈ I, ∈,), a (o) 101 『 ≤ · (5). Therefore, the establishment of the lemma . The following give an example to illustrate the main theorems. Down Let X-Y-R. Consider the equation family (,) △ Bz + h +(,)= 0. Where B =; 010000001 (12) and lllf + I51. I (13) and for each port ∈ J,: × First C mapping, { : port ∈ I) are uniformly bounded on the × and other degrees with 4 Xie Bihua : Single of nonlinear equations and the intrinsic Value differences continue , plant. (,。)= 0, D,. (,。)= 0. You know = l is the intrinsic value of single- B , and = 1 corresponding to f01 intrinsic element is o-l01. Which verifies all the conditions to meet the theorem , so a 1 is the evolution equations (13 ) points of public discrimination , and 【 1J. Exist (1, O) ∈ R × R of a neighborhood uo, such that for each ∈ I, (13) is exactly the solution in the composition of the two curves . 1234