The Gronwall Type Lemmas and Applications |
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Contents
Introduction | 1 |
3 Convergence to Zero Conditions for the Solutions | 24 |
2 Estimations for the Solutions of Volterra Integral | 38 |
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Applying lemma L.1.1.1 approximation is uniformly assume the kernel asymptotically stable Banach space boundedness Cauchy problem conditions 2.9 consider the integral convergence to zero convergente to zero differential equations du)ds equivalent with g exists a function following assertions following conditions following estimation function f satisfies function f verifies fundamental matrix G of integral holds integral inequation 1.1 kernel G kernel V satisfies Lemma of estimation Let consider Let now suppose Let suppose lim U(t M₁ M₂ nonnegative continuous solutions number of Corollaries omit the details proof follows relation G relation L-VV relation S-U result is embodied s)ds satisfies the condition satisfies the relation solution of 1.1 solution of A;f solution of Cauchy Solutions of Volterra telt theorem is proved tion trivial solution uniformly bounded uniformly convergente uniformly stable verifies the condition verifies the relation Volterra integral equations xoll zero to infinite