- 期刊
ON THE QUASIUNIQUENESS OF SOLUTIONS OF DEGENEFIATE EQUATIONS IN HILBERT SPACE
摘要
In this paper, we study the quasiuniqueness (i.e., f_1=f_2 if f_1-f_2 is flat, the function f(t) being called flat if, for any K＞0, t^(-k) f(t)→0 as t→0) for ordinary differential equations in Hilbert space. The case of inequalities is studied, too. The most important result of this paper is this: THEOREM 3. Let B(t) be a linear operator with domain D_B and B(t)=B_1(t)+B_2(t) where (B_1(t)x, x) is real and Re(B_2(t)x, x)=0 for any x ∈ D_B. Let for any x ∈ D_B the following estimate hold: (The equation is abbreviated) with C≥0. If u(t) is a smooth flat solution of the following inequality in the interval t ∈ I=(0,1]. (The equation is abbreviated) with non-negative continuous function φ(t), then u(t)≡0 in I. One example with self-adjoint B(t) is given, too.
延伸閱讀
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